scispace - formally typeset
Search or ask a question

Showing papers on "Semiparametric model published in 2022"


Journal ArticleDOI
TL;DR: In this article , a semiparametric model averaging prediction (SMAP) method for a dichotomous response is proposed to approximate the unknown score function by a linear combination of one-dimensional marginal score functions.

14 citations


Journal ArticleDOI
TL;DR: In this article , the authors proposed using Mishra, Su, Ullah's (2010) semiparametric variance to estimate Value at Risk (VaR) and Expected Shortfall (ES).

3 citations


Journal ArticleDOI
TL;DR: This article proposed a variable selection procedure that is suitable for the estimation methods based on pseudo-score functions and investigated the asymptotic properties of penalized estimators and conduct simulation studies to illustrate the theoretical results.
Abstract: A common issue in longitudinal studies is that subjects' visits are irregular and may depend on observed outcome values which is known as longitudinal data with informative observation times (follow‐up). Semiparametric regression modeling for this type of data has received much attention as it provides more flexibility in studying the association between regression factors and a longitudinal outcome. An important problem here is how to select relevant variables and estimate their coefficients in semiparametric regression models when the number of covariates at baseline is large. The current penalization procedures in semiparametric regression models for longitudinal data do not account for informative observation times. We propose a variable selection procedure that is suitable for the estimation methods based on pseudo‐score functions. We investigate the asymptotic properties of penalized estimators and conduct simulation studies to illustrate the theoretical results. We also use the procedure for variable selection in semiparametric regression models for the STAR*D dataset from a multistage randomized clinical trial for treating major depressive disorder.

3 citations


Journal ArticleDOI
TL;DR: In this article , a combination of parametric and nonparametric regression models, parametric estimates, fit statistical values of the models, confidence intervals and standard error values were calculated.
Abstract: Parametric regression models assume that the dependent variable is a linear relationship with the independent variables and the form of the relationship is known. Nonparametric regression methods are applied in cases where the relationship type is not known or assumptions cannot be provided. However, when there is more than one independent variable, some of the independent variables may be in a linear relationship with the dependent variable, while some may be in a nonlinear relationship. In order to model these variables, semiparametric regression models, which are a combination of parametric and nonparametric regression methods, are used. In this study parametric, nonparametric and semiparametric regression models, parametric estimates, fit statistical values of the models, confidence intervals and standard error values were calculated. As a result of the analysis, the parameters of the milking unit and the quarantine area among the parametric variables, the operation area, the ventilation area, the number of ventilation, the quarantine area, the infirmary area, the manure pit and the distance to the center among the non-parametric variables were found to be statistically very important (P

3 citations


ReportDOI
08 Mar 2022
TL;DR: In this article , the Generalized Method of Moments (GMM) framework is used to address the EIV problem in the setting where the variability of the variance is a fraction of that of the mismeasured variables.
Abstract: We develop a practical way of addressing the Errors-In-Variables (EIV) problem in the Generalized Method of Moments (GMM) framework. We focus on the settings in which the variability of the EIV is a fraction of that of the mismeasured variables, which is typical for empirical applications. For any initial set of moment conditions our approach provides a corrected set of moment conditions that are robust to the EIV. We show that the GMM estimator based on these moments is root-n-consistent, with the standard tests and confidence intervals providing valid inference. This is true even when the EIV are so large that naive estimators (that ignore the EIV problem) may be heavily biased with the confidence intervals having 0% coverage. Our approach involves no nonparametric estimation, which is particularly important for applications with multiple covariates, and settings with multivariate, serially correlated, or non-classical EIV.

3 citations


Journal ArticleDOI
TL;DR: In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website as mentioned in this paper , in case of legitimate complaints the material will be removed.
Abstract: Disclaimer/Complaints regulations If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: https://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.

2 citations


Journal ArticleDOI
TL;DR: In this paper , a semiparametric Bayesian model is proposed to detect biclusters, subsets of individuals sharing similar patterns over a set of conditions, which is based on the well-known plaid model by Lazzeroni and Owen.
Abstract: Motivated by classes of problems frequently found in the analysis of gene expression data, we propose a semiparametric Bayesian model to detect biclusters, that is, subsets of individuals sharing similar patterns over a set of conditions. Our approach is based on the well-known plaid model by Lazzeroni and Owen (2002). By assuming a truncated stick-breaking prior we also find the number of biclusters present in the data as part of the inference. Evidence from a simulation study shows that the model is capable of correctly detecting biclusters and performs well compared to some competing approaches. The flexibility of the proposed prior is demonstrated with applications to the analysis of gene expression data (continuous responses) and histone modifications data (count responses).

2 citations


Journal ArticleDOI
TL;DR: In this article , a spatial autoregressive stochastic frontier model with smooth coefficients is proposed to estimate the technical efficiencies of Chinese chemical firms from 2004-2006. But the model is not suitable for the estimation of the spillover effects.

2 citations


Journal ArticleDOI
TL;DR: A semiparametric factor model with minimal parametric assumptions is proposed, in which the main effect and interaction functions are approximated by cubic splines for the log conditional densities of the manifest variables.

2 citations


DissertationDOI
13 Jun 2022
TL;DR: In this article , the performance of various bandwidth selectors in the local linear regression method was investigated and the results indicated that the variable bandwidth selector is superior to constant bandwidth selector in the more skewed data set or complicated functional form.
Abstract: This dissertation is primary concerned on the study of semiparametric estimation approaches. In the respect of the usage of econometric analysis that is evaluating theoretical relationship, the semiparametric analysis is useful to get the flexibility of functional form. The kernel-type nonparametric methods are used for semiparametric approaches in this dissertation. The first essay focuses upon performance of various bandwidth selectors in the local linear regression method. The results indicate that the variable bandwidth selector is superior to constant bandwidth selector in the more skewed data set or complicated functional form. LSCV bandwidth selector fit well in the simple functional form. This essay also indicates that the variable bandwidth selector performs well in almost everywhere in general. The second essay is the application of local linear regression method with variable bandwidth selector to the wage equation. The challenge for the quadratic or quartic relationship between log wage and experience recently make possible to apply the semiparametric estimation method to the wage equation. The comparison of semiparametric and parametric specifications indicates that semiparametric estimation methods capture nonlinearities in the earnings profiles. Also, the analysis of wage profile using semiparametric method confirms the stylized facts of U.S. earning profiles during the 1990's. The semiparametric estimation method is applied to the qualitative response model in the third essay. The simultaneous two-stage probit model is studied using semiparametric method in the two-stage. Klein and Spady's semiparametric MLE is applied in this essay. The Monte Carlo simulation results indicate that semiparametric method performs well in the both homoscedasticity and heteroscedasticity error terms. MSE of semiparametric estimation is smaller and steadier than two-stage probit estimation.

2 citations


Journal ArticleDOI
TL;DR: In this paper , the authors proposed a penalized version of the semiparametric estimation approach, which exploits the fact that the innovation distribution is often considered to be smooth, i.e. two consecutive entries of the PMF differ only slightly from each other.
Abstract: Abstract Popular models for time series of count data are integer-valued autoregressive (INAR) models, for which the literature mainly deals with parametric estimation. In this regard, a semiparametric estimation approach is a remarkable exception which allows for estimation of the INAR models without any parametric assumption on the innovation distribution. However, for small sample sizes, the estimation performance of this semiparametric estimation approach may be inferior. Therefore, to improve the estimation accuracy, we propose a penalized version of the semiparametric estimation approach, which exploits the fact that the innovation distribution is often considered to be smooth, i.e. two consecutive entries of the PMF differ only slightly from each other. This is the case, for example, in the frequently used INAR models with Poisson, negative binomially or geometrically distributed innovations. For the data-driven selection of the penalization parameter, we propose two algorithms and evaluate their performance. In Monte Carlo simulations, we illustrate the superiority of the proposed penalized estimation approach and argue that a combination of penalized and unpenalized estimation approaches results in overall best INAR model fits.

Journal ArticleDOI
TL;DR: It is demonstrated that the resized bootstrap method yields valid confidence intervals in both simulated and real data examples, and the methods extend to other high-dimensional generalized linear models.
Abstract: Accurate statistical inference in logistic regression models remains a critical challenge when the ratio between the number of parameters and sample size is not negligible. This is because approximations based on either classical asymptotic theory or bootstrap calculations are grossly off the mark. This paper introduces a resized bootstrap method to infer model parameters in arbitrary dimensions. As in the parametric bootstrap, we resample observations from a distribution, which depends on an estimated regression coefficient sequence. The novelty is that this estimate is actually far from the maximum likelihood estimate (MLE). This estimate is informed by recent theory studying properties of the MLE in high dimensions, and is obtained by appropriately shrinking the MLE towards the origin. We demonstrate that the resized bootstrap method yields valid confidence intervals in both simulated and real data examples. Our methods extend to other high-dimensional generalized linear models.

Journal ArticleDOI
TL;DR: In this paper , the authors considered a multivariate response regression model where each coordinate is described by a location-scale non- or semiparametric regression and the dependence structure of the noise term is represented by a parametric copula.
Abstract: We consider a multivariate response regression model where each coordinate is described by a location-scale non- or semiparametric regression and where the dependence structure of the “noise term” is described by a parametric copula. Our goal is to estimate the associated Euclidean copula parameter, given a sample of the response and the covariate. In the absence of the copula sample, the usual oracle ranks are no longer computable. Instead, we study the normal scores estimator for the Gaussian copula and generalized pseudo-likelihood estimation for general parametric copulas, both based on residual ranks calculated from preliminary non- or semiparametric estimators of the location and scale functions. We show that the residual-based estimators are asymptotically equivalent to their oracle counterparts and provide explicit rate of convergence. Partially to serve this objective, we also study weighted convergence of the residual empirical process under the non- or semiparametric regression model.

Journal ArticleDOI
24 Jun 2022
TL;DR: In this paper , the effect of schooling years on wage level in Turkey by using the Mincer wage equation was evaluated by using a semiparametric regression model considering the control function approach.
Abstract: This study aims to evaluate the effect of schooling years on wage level in Turkey by using the Mincer wage equation. This function is used as the baseline for the investigation of earnings determinants. For this purpose, the relationship between wage and education level of people is estimated by using a semiparametric regression model considering the control function approach. Various variables such as education level, experience, gender and marital status are estimated separately in the wage model by utilizing the Household Budget Statistics micro data set of 2017 in Turkey obtained by the Turkish Statistical Institute. The parametric model does not clarify the model clearly when functional form of relation is not known. To overcome this drawback, semiparametric regression model, which contains parametric and nonparametric variables, can be successfully applied. This model is extended by adding the 1997 education reform as a control variable. The achieved semiparametric test results from this study showed that there is a positive relationship between schooling years and wage level. On the other hand, control function approach results indicate the existence of fluctuant progress for the effect of schooling years on the wage level along the period.

Journal ArticleDOI
TL;DR: In this paper, a maximum full semiparametric likelihood estimation method was proposed for non-ignorable missing data, which is an efficient combination of the parametric conditional likelihood and the marginal nonparametric biased sampling likelihood.
Abstract: During the past few decades, missing-data problems have been studied extensively, with a focus on the ignorable missing case, where the missing probability depends only on observable quantities. By contrast, research into non-ignorable missing data problems is quite limited. The main difficulty in solving such problems is that the missing probability and the regression likelihood function are tangled together in the likelihood presentation, and the model parameters may not be identifiable even under strong parametric model assumptions. In this paper we discuss a semiparametric model for non-ignorable missing data and propose a maximum full semiparametric likelihood estimation method, which is an efficient combination of the parametric conditional likelihood and the marginal nonparametric biased sampling likelihood. The extra marginal likelihood contribution can not only produce efficiency gain but also identify the underlying model parameters without additional assumptions. We further show that the proposed estimators for the underlying parameters and the response mean are semiparametrically efficient. Extensive simulations and a real data analysis demonstrate the advantage of the proposed method over competing methods.

Journal ArticleDOI
TL;DR: In this paper , sufficient conditions for preservation of several transform orders under a typical family of semiparametric distributions are made, and the preservation properties are developed to compare mixture semi-parametric distributions.

Journal ArticleDOI
TL;DR: In this article , the authors extended the robust semiparametric ordinal regression model to estimate regional treatment effects, in which the regression coefficients and regional effects are modeled parametrically for ease of interpretation, and the regression link function is specified nonparametrically.
Abstract: ABSTRACT Global clinical trials involving multiple regions are common in current drug development processes. Determining the regional treatment effects of a new therapy over an existing therapy is important to both the sponsors and the regulatory agencies in the regions. Existing methods are mainly for continuous primary endpoints and use subjectively specified models, which may deviate from the true model. Here, we consider trials that have ordinal responses as the primary endpoint. This article extends the recently developed robust semiparametric ordinal regression model to estimate regional treatment effects, in which the regression coefficients and regional effects are modeled parametrically for ease of interpretation, and the regression link function is specified nonparametrically for robustness. The model parameters are estimated by semiparametric maximum likelihood estimation, and the null hypothesis of no regional effect is tested by the Wald test. Simulation studies are conducted to evaluate the performance of the proposed method and compare it with the commonly used parametric model. The results of the former show an improved overall performance over the latter. In particular, the model yields much higher precision in estimation and prediction than the fixed-link model. This result is especially appealing since our interest is to estimate the treatment effect more efficiently and the estimand is of particular interest in multiregional clinical trials. We then apply the method by analyzing real multiregional clinical trials with ordinal responses as their primary endpoint.

Journal ArticleDOI
TL;DR: In this article , a semiparametric maximum likelihood approach is proposed to fit logistic regression models to data arising from the two-phase stratified case-control sampling design, where a subset of covariates are available only for a portion of cases and controls who are selected based on the case- control status and fully collected covariates.
Abstract: We study statistical inference methods for fitting logistic regression models to data arising from the two-phase stratified case-control sampling design, where a subset of covariates are available only for a portion of cases and controls who are selected based on the case-control status and fully collected covariates. We are additionally interested in characterizing the distribution of incomplete covariates conditional on fully observed ones. It is desirable to include all subjects in the analysis to achieve consistency of parameter estimation and optimal statistical efficiency. We develop a semiparametric maximum likelihood approach under the rare disease assumption, where parameter estimates are obtained through a novel reparametrized profile likelihood technique. We study the large sample distribution theory for the proposed estimator, and demonstrate through simulation studies that it performs well in finite samples and has improved statistical efficiency compared with existing approaches. We apply the proposed method to analyze a stratified case-control study of breast cancer nested ∗ Co-first authors ∗∗ Corresponding author Statistica Sinica: Newly accepted Paper (accepted author-version subject to English editing)

Journal ArticleDOI
TL;DR: In this article , a new combined semiparametric estimator of the conditional variance is proposed, which takes the product of a parametric estimators and a nonparametric estimation based on machine learning.
Abstract: This paper proposes a new combined semiparametric estimator of the conditional variance that takes the product of a parametric estimator and a nonparametric estimator based on machine learning. A popular kernel-based machine learning algorithm, known as the kernel-regularized least squares estimator, is used to estimate the nonparametric component. We discuss how to estimate the semiparametric estimator using real data and how to use this estimator to make forecasts for the conditional variance. Simulations are conducted to show the dominance of the proposed estimator in terms of mean squared error. An empirical application using S&P 500 daily returns is analyzed, and the semiparametric estimator effectively forecasts future volatility.

Journal ArticleDOI
TL;DR: In this article , the authors proposed an innovative semiparametric method consisting of two modeling components: the nonparametric estimation and copula method for each marginal distribution of the portfolio and their joint distribution, respectively.
Abstract: Tail risk is a classic topic in stressed portfolio optimization to treat unprecedented risks, while the traditional mean-variance approach may fail to perform well. This study proposes an innovative semiparametric method consisting of two modeling components: the nonparametric estimation and copula method for each marginal distribution of the portfolio and their joint distribution, respectively. We then focus on the optimal weights of the stressed portfolio and its optimal scale beyond the Gaussian restriction. Empirical studies include statistical estimation for the semiparametric method, risk measure minimization for optimal weights, and value measure maximization for the optimal scale to enlarge the investment. From the outputs of short-term and long-term data analysis, optimal stressed portfolios demonstrate the advantages of model flexibility to account for tail risk over the traditional mean-variance method.

Journal ArticleDOI
TL;DR: In this paper , a model for cross-over designs with repeated measures within each period was developed using an extension of generalized estimating equations that includes a parametric component to model treatment effects and a non-parametric component based on splines.
Abstract: A model for cross-over designs with repeated measures within each period was developed. It was obtained using an extension of generalized estimating equations that includes a parametric component to model treatment effects and a non-parametric component to model time and carry-over effects; the estimation approach for the non-parametric component is based on splines. A simulation study was carried out to explore the model properties. Thus, when there is a carry-over effect or a functional temporal effect, the proposed model presents better results than the standard models. Among the theoretical properties, the solution is found to be analogous to weighted least squares. Therefore, model diagnostics can be made by adapting the results from a multiple regression. The proposed methodology was implemented in the data sets of the cross-over experiments that motivated the approach of this work: systolic blood pressure and insulin in rabbits.

Journal ArticleDOI
TL;DR: The results indicated that the semiparametric models outperform linear polynomial regression approximations to predict the behavior of response variables in non-linear settings.
Abstract: This work introduces a straightforward framework for semiparametric non-linear models as an alternative to existing non-linear parametric models, whose interpretation primarily depends on biological or physical aspects that are not always available in every practical situation. The proposed methodology does not require intensive numerical methods to obtain estimates in non-linear contexts, which is attractive as such algorithms’ convergence strongly depends on assigning good initial values. Moreover, the proposed structure can be compared with standard polynomial approximations often used for explaining non-linear data behaviors. Approximate posterior inferences for the semiparametric model parameters were obtained from a fully Bayesian approach based on the Metropolis-within-Gibbs algorithm. The proposed structures were considered to analyze artificial and real datasets. Our results indicated that the semiparametric models outperform linear polynomial regression approximations to predict the behavior of response variables in non-linear settings.

Journal ArticleDOI
TL;DR: A flexible Bayesian semiparametric approach to covariate informed multivariate deconvolution of densities, which allows the joint and the marginal densities to vary flexibly with the associated predictors but also allows automatic selection of the most influential predictors.
Abstract: Abstract Estimating the marginal and joint densities of the long-term average intakes of different dietary components is an important problem in nutritional epidemiology. Since these variables cannot be directly measured, data are usually collected in the form of 24-hour recalls of the intakes. The problem of estimating the density of the latent long-term average intakes from their observed but error contaminated recalls then becomes a problem of multivariate deconvolution of densities. The underlying densities could potentially vary with the subjects’ demographic characteristics such as sex, ethnicity, age, etc. The problem of density deconvolution in the presence of associated precisely measured covariates has, however, never been considered before, not even in the univariate setting. We present a flexible Bayesian semiparametric approach to covariate informed multivariate deconvolution. Building on recent advances on copula deconvolution and conditional tensor factorization techniques, our proposed method not only allows the joint and the marginal densities to vary flexibly with the associated predictors but also allows automatic selection of the most influential predictors. Importantly, the method also allows the density of interest and the density of the measurement errors to vary with potentially different sets of predictors. We design Markov chain Monte Carlo algorithms that enable efficient posterior inference, appropriately accommodating uncertainty in all aspects of our analysis. The empirical efficacy of the proposed method is illustrated through simulation experiments. Its practical utility is demonstrated in the afore-described nutritional epidemiology applications in estimating covariate adjusted long term intakes of different dietary components. An important by-product of the approach is a solution to covariate informed ordinary multivariate density estimation. Supplementary materials include substantive additional details and R codes are also available online.

Journal ArticleDOI
TL;DR: In this paper , the authors study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise, and propose a dynamic statistical learning and decision making policy that minimizes regret (maximizes revenue) by combining semiparametric estimation for a generalized linear model with unknown link and online decision making.
Abstract: In this article, we study the contextual dynamic pricing problem where the market value of a product is linear in its observed features plus some market noise. Products are sold one at a time, and only a binary response indicating success or failure of a sale is observed. Our model setting is similar to the work by? except that we expand the demand curve to a semiparametric model and learn dynamically both parametric and nonparametric components. We propose a dynamic statistical learning and decision making policy that minimizes regret (maximizes revenue) by combining semiparametric estimation for a generalized linear model with unknown link and online decision making. Under mild conditions, for a market noise cdf F(·) with mth order derivative ( m≥2), our policy achieves a regret upper bound of O˜d(T2m+14m−1), where T is the time horizon and O˜d is the order hiding logarithmic terms and the feature dimension d. The upper bound is further reduced to O˜d(T) if F is super smooth. These upper bounds are close to Ω(T), the lower bound where F belongs to a parametric class. We further generalize these results to the case with dynamic dependent product features under the strong mixing condition. Supplementary materials for this article are available online.

Journal ArticleDOI
TL;DR: In this paper, the authors address the problem of imputation when a response or covariate may be subject to a nonignorable (or, equivalently, missing not at random) nonresponse, meaning the response probability may depend on a variable that is not always observed.
Abstract: We address the problem of imputation when a response or covariate may be subject to a nonignorable (or, equivalently, missing not at random) nonresponse, meaning the response probability may depend on a variable that is not always observed. We discuss model identification and develop a novel estimator of the parameters of the response probability. We use a propensity score adjustment to incorporate a subset for which both the response and the covariate are missing. We derive an approximation for the large-sample variance and assess the finite-sample properties of the variance estimator using simulations. The simulation results also show that a quantile regression offers a compromise between fully parametric and nonparametric alternatives. In an application to data from a 2011 survey of pet owners, a quantile regression allows us to model complex relations between two types of veterinary expenditures, where we find evidence a of nonignorable nonresponse.

Journal ArticleDOI
01 Oct 2022
TL;DR: In this article , a new flexible semiparametric propensity score model was proposed where the relationship between the missingness indicator and the partially observed response was totally unspecified and estimated nonparametrically, while the relationship was modeled parametrically.
Abstract: Consider the regression setting where the response variable is subject to missing data and the covariates are fully observed. A nonignorable propensity score model, i.e., the probability that the response is observed conditional on all variables depends on the missing values themselves, is assumed throughout the paper. In such problems, model misspecification and model identifiability are two critical issues. A fully parametric approach can produce results that are sensitive to the model assumptions, while a fully nonparametric approach may not be sufficient for model identification. A new flexible semiparametric propensity score model is proposed where the relationship between the missingness indicator and the partially observed response is totally unspecified and estimated nonparametrically, while the relationship between the missingness indicator and the fully observed covariates is modeled parametrically. The proposed estimator is constructed via a semiparametric treatment and is proved to be semiparametrically efficient. Comprehensive simulation studies are conducted to examine the finite-sample performance of the estimators. While the naive parametric method leads to heavily biased estimator and poor coverage results, the proposed method produces estimator with negligible finite-sample biases and also correct inference results. The proposed method is further illustrated via an electronic health records (EHR) data application for the albumin level in the blood sample. The empirical analyses demonstrated that the proposed semiparametric propensity score model is more sensible than a purely parametric model. The proposed method could be very useful to uncover the unknown and possibly nonlinear dependence of the propensity score model to the albumin level, and is recommended for practical use.

Journal ArticleDOI
TL;DR: In this paper , a panel multinomial choice model with bundles is proposed to identify substitution patterns between two goods using the Nielsen data, which is shown to perform more robustly than the parametric method through Monte Carlo simulations.
Abstract: This paper studies semiparametric identification of substitution patterns between two goods using a panel multinomial choice model with bundles. My model allows the two goods to be either substitutes or complements and admits heterogeneous complementarity through observed characteristics. I characterize the sharp identified set for the model parameters and provide sufficient conditions for point identification. My identification analysis accommodates endogenous covariates through flexible dependence structures between observed characteristics and fixed effects while placing no distributional assumptions on unobserved preference shocks. My method is shown to perform more robustly than the parametric method through Monte Carlo simulations. As an empirical illustration, I apply my method to estimate substitution patterns between cigarettes and e-cigarettes using the Nielsen data.

Posted ContentDOI
Taku Moriyama1
14 Jun 2022
TL;DR: In this paper , the authors constructed two types of semiparametric distribution estimators of sample maximums by mixing the two distributions presented in Moriyama (2021) and this paper .
Abstract: Several approaches of nonparametric inference for extreme values have been studied. This study surveys the semiparametric probability distribution estimation of sample maximums. Moriyama (2021) clarified that the parametric fitting to the generalized extreme value distribution becomes large as the tail becomes light, which means the convergence becomes slow. Moriyama (2021) proposed a nonparametric distribution estimator without the fitting of the distribution and obtained asymptotic properties. The nonparametric estimator was proved to outperform the parametrically fitting estimator for light-tailed data. Moreover, it was demonstrated that the parametric fitting estimator numerically outperformed the nonparametric one in other cases. Motivated by the study, we construct two types of semiparametric distribution estimators of sample maximums. The proposed distribution estimators are constructed by mixing the two distribution estimators presented in Moriyama (2021). The cross-validation method and the maximum-likelihood method are presented as a way of estimating the optimal mixing ratio. Simulation experiments clarify the numerical properties of the two types of semiparametric distribution estimators.

Journal ArticleDOI
TL;DR: In this article , nonlinear and semiparametric extensions of the dynamic linear regression model are explored to allow unknown forms of nonlinearities in the regression function, and performance comparison among these semi-parametric AR models and the linear AR model are carried out via their application to Australian data on growth in GDP and unemployment using RMSE and GCV measures.
Abstract: Dynamic linear regression models are used widely in applied econometric research. Most applications employ linear autoregressive (AR) models, distributed lag (DL) models or autoregressive distributed lag (ARDL) models. These models, however, perform poorly for data sets with unknown, complex nonlinear patterns. This paper studies nonlinear and semiparametric extensions of the dynamic linear regression model and explores the autoregressive (AR) extensions of two semiparametric techniques to allow unknown forms of nonlinearities in the regression function. The autoregressive GAM (GAM-AR) and autoregressive multivariate adaptive regression splines (MARS-AR) studied in the paper automatically discover and incorporate nonlinearities in autoregressive (AR) models. Performance comparisons among these semiparametric AR models and the linear AR model are carried out via their application to Australian data on growth in GDP and unemployment using RMSE and GCV measures. Â

Book ChapterDOI
01 Jan 2022
TL;DR: In this paper , a review of parametric, nonparametric, and locally parametric techniques for time series is presented. But the focus of the review is on Gaussian and elliptic distributions.
Abstract: In this chapter, we give a very brief but up-to-date review of parametric, nonparametric, and locally parametric techniques that forms the background for the main topics of the book. Among topics discussed, there are distributional aspects such as Gaussian and elliptic distributions. Next, parametric regression models, linear, and nonlinear are covered. A compressed version of time series models, including ARMA, GARCH, and nonlinear models, is included. The last part of the chapter deals with nonparametric methods in density estimation, regression estimation, bandwidth choice, and the curse of dimensionality. Additive models, quantile regression, and semiparametric models are also mentioned. Finally, locally parametric models are introduced as leading up to local Gaussian approximations, which are the main topic of the book.