Showing papers on "Semiparametric model published in 2018"
TL;DR: A novel estimation method for estimating unknown contact forces exerted on a robot manipulator called disturbance Kalman filter (DKF) that can provide robust and accurate estimation against uncertainty is presented.
Abstract: Force estimation methods enable robots to interact with the environment or humans compliantly and safely without additional sensing device. In this paper, we present a novel method for estimating unknown contact forces exerted on a robot manipulator. The force estimation method is divided into two steps. The first step is to identify a robot dynamics model. A parametric model is derived first based on rigid-body dynamic (RBD) theory. To improve the model accuracy, a nonparametric compensator trained with multilayer perception (MLP) is added to compensate for errors of the RBD model. The result is a semiparametric model that provides better model accuracy than either the RBD model or the MLP model alone. The second step is to construct a force estimation observer. A novel estimation method called disturbance Kalman filter (DKF) is developed in this paper. The design of DKF based on a time-invariant composite system model is presented. DKF can take both manipulator's dynamics model and disturbance's dynamics model into account. As with Kalman filter, it can provide robust and accurate estimation against uncertainty. Simulation and experimental results, obtained using a six-degrees-of-freedom Kinova Jaco2 manipulator, demonstrate the effectiveness of the proposed method.
74 citations
TL;DR: In this paper, an extension of the stochastic block model for recurrent interaction events in continuous time is proposed, where every individual belongs to a latent group and conditional interactions between two individuals follow an inhomogeneous Poisson process with intensity driven by the individuals' latent groups.
Abstract: We propose an extension of the stochastic block model for recurrent interaction events in continuous time, where every individual belongs to a latent group and conditional interactions between two individuals follow an inhomogeneous Poisson process with intensity driven by the individuals’ latent groups. We show that the model is identifiable and estimate it with a semiparametric variational expectation-maximization algorithm. We develop two versions of the method, one using a nonparametric histogram approach with an adaptive choice of the partition size, and the other using kernel intensity estimators. We select the number of latent groups by an integrated classification likelihood criterion. We demonstrate the performance of our procedure on synthetic experiments, analyse two datasets to illustrate the utility of our approach, and comment on competing methods.
62 citations
TL;DR: In this paper, the authors proposed two semi-parametric model averaging schemes for nonlinear dynamic time series regression models with a very large number of covariates including exogenous regressors and auto-regressive lags.
Abstract: We propose two semiparametric model averaging schemes for nonlinear dynamic time series regression models with a very large number of covariates including exogenous regressors and auto-regressive lags. Our objective is to obtain more accurate estimates and forecasts of time series by using a large number of conditioning variables in a nonparametric way. In the first scheme, we introduce a Kernel Sure Independence Screening (KSIS) technique to screen out the regressors whose marginal regression (or auto-regression) functions do not make a significant contribution to estimating the joint multivariate regression function; we then propose a semiparametric penalized method of Model Averaging MArginal Regression (MAMAR) for the regressors and auto-regressors that survive the screening procedure, to further select the regressors that have significant effects on estimating the multivariate regression function and predicting the future values of the response variable. In the second scheme, we impose an app...
53 citations
TL;DR: The Wiener process is used to model product degradation, and the group-specific random environments are captured using a stochastic time scale and both semiparametric and parametric estimation procedures are developed for the model.
Abstract: Degradation studies are often used to assess reliability of products subject to degradation-induced soft failures. Because of limited test resources, several test subjects may have to share a test rig and have their degradation measured by the same operator. The common environments experienced by subjects in the same group introduce significant interindividual correlations in their degradation, which is known as the block effect. In the present article, the Wiener process is used to model product degradation, and the group-specific random environments are captured using a stochastic time scale. Both semiparametric and parametric estimation procedures are developed for the model. Maximum likelihood estimations of the model parameters for both the semiparametric and parametric models are obtained with the help of the EM algorithm. Performance of the maximum likelihood estimators is validated through large sample asymptotics and small sample simulations. The proposed models are illustrated by an appl...
49 citations
TL;DR: In this paper, the authors considered parametric and semi-parametric spatial hedonic model variants that account for spatial autocorrelation, spatial heterogeneity and (smooth and nonparametrically specified) nonlinearities using penalized splines methodology.
Abstract: House price prediction is a hot topic in the economic literature. House price prediction has traditionally been approached using a-spatial linear (or intrinsically linear) hedonic models. It has been shown, however, that spatial effects are inherent in house pricing. This article considers parametric and semi-parametric spatial hedonic model variants that account for spatial autocorrelation, spatial heterogeneity and (smooth and nonparametrically specified) nonlinearities using penalized splines methodology. The models are represented as a mixed model that allow for the estimation of the smoothing parameters along with the other parameters of the model. To assess the out-of-sample performance of the models, the paper uses a database containing the price and characteristics of 10,512 homes in Madrid, Spain (Q1 2010). The results obtained suggest that the nonlinear models accounting for spatial heterogeneity and flexible nonlinear relationships between some of the individual or areal characteristics of the houses and their prices are the best strategies for house price prediction.
39 citations
TL;DR: The authors proposed a semi-parametric identification and estimation approach to multinomial choice models in a panel data setting with individual fixed effects based on cyclic monotonicity, which is a defining convexanalytic feature of the random utility framework underlying multivariate choice models.
Abstract: This paper proposes a new semi‐parametric identification and estimation approach to multinomial choice models in a panel data setting with individual fixed effects. Our approach is based on cyclic monotonicity, which is a defining convex‐analytic feature of the random utility framework underlying multinomial choice models. From the cyclic monotonicity property, we derive identifying inequalities without requiring any shape restrictions for the distribution of the random utility shocks. These inequalities point identify model parameters under straightforward assumptions on the covariates. We propose a consistent estimator based on these inequalities.
38 citations
22 May 2018
TL;DR: In this paper, a hedonic price function built through a semiparametric additive model is tried out for the real estate market analysis of the central area of Reggio Calabria.
Abstract: In this paper a hedonic price function built through a semiparametric additive model is tried out for the real estate market analysis of the central area of Reggio Calabria. The semiparametric model uses Penalized Spline functions and aims to achieve an improvement in the prediction of the market prices of housing properties in the central area of Reggio Calabria. More in particular, the final objective of the research is to detect and to identify possible potential market premium in real estate exchange and rent markets for green buildings. This is the first preliminary phase for the unavoidable verification of the robustness of the real estate sample, or for the subsequent individuation of progressive real estate sub-samples.
30 citations
TL;DR: It is demonstrated that these parametric within-subject approaches may produce false positives and biased parameter estimates if the assumption concerning the response time distribution is violated.
Abstract: In item response theory, modelling the item response times in addition to the item responses may improve the detection of possible between- and within-subject differences in the process that resulted in the responses. For instance, if respondents rely on rapid guessing on some items but not on all, the joint distribution of the responses and response times will be a multivariate within-subject mixture distribution. Suitable parametric methods to detect these within-subject differences have been proposed. In these approaches, a distribution needs to be assumed for the within-class response times. In this paper, it is demonstrated that these parametric within-subject approaches may produce false positives and biased parameter estimates if the assumption concerning the response time distribution is violated. A semi-parametric approach is proposed which resorts to categorized response times. This approach is shown to hardly produce false positives and parameter bias. In addition, the semi-parametric approach results in approximately the same power as the parametric approach.
27 citations
TL;DR: This work proposes a new varying-coefficient semiparametric model averaging prediction (VC-SMAP) approach to analyze large data sets with abundant covariates, which provides more flexibility than parametric methods, while being more stable and easily implemented than fully multivariate nonparametric varying- coefficient models.
Abstract: Forecasting and predictive inference are fundamental data analysis tasks. Most studies employ parametric approaches making strong assumptions about the data generating process. On the other hand, while nonparametric models are applied, it is sometimes found in situations involving low signal to noise ratios or large numbers of covariates that their performance is unsatisfactory. We propose a new varying-coefficient semiparametric model averaging prediction (VC-SMAP) approach to analyze large data sets with abundant covariates. Performance of the procedure is investigated with numerical examples. Even though model averaging has been extensively investigated in the literature, very few authors have considered averaging a set of semiparametric models. Our proposed model averaging approach provides more flexibility than parametric methods, while being more stable and easily implemented than fully multivariate nonparametric varying-coefficient models. We supply numerical evidence to justify the effectiveness of our methodology.
27 citations
TL;DR: In this paper, a new semiparametric quantile panel data model with correlated random effects is proposed, in which some of the coefficients are allowed to depend on some smooth economic variables while other coefficients remain constant, and a three-stage estimation procedure is proposed to estimate both constant and functional coefficients and their asymptotic properties are investigated.
26 citations
TL;DR: This contribution represents the start of a new era for semiparametric regression, where large and complex analyses are performed via fast Bayesian inference methodology and software, mainly being developed within Machine Learning.
Abstract: We provide several examples of Bayesian semiparametric regression analysis via the Infer.NET package for approximate deterministic inference in Bayesian models. The examples are chosen to encompass a wide range of semiparametric regression situations. Infer.NET is shown to produce accurate inference in comparison with Markov chain Monte Carlo via the BUGS package, but to be considerably faster. Potentially, this contribution represents the start of a new era for semiparametric regression, where large and complex analyses are performed via fast Bayesian inference methodology and software, mainly being developed within Machine Learning.
TL;DR: In this paper, a semiparametric model is proposed to describe ADDT data, which not only provides flexible models with few assumptions but also retains the physical meaning of degradation mechanisms (e.g., the degradation path is monotonic).
Abstract: Accelerated destructive degradation tests (ADDT) are widely used in industry to evaluate materials’ long-term properties. Even though there has been tremendous statistical research in nonparametric methods, the current industrial practice is still to use application-specific parametric models to describe ADDT data. The challenge of using a nonparametric approach comes from the need to retain the physical meaning of degradation mechanisms and also perform extrapolation for predictions at the use condition. Motivated by this challenge, we propose a semiparametric model to describe ADDT data. We use monotonic B-splines to model the degradation path, which not only provides flexible models with few assumptions, but also retains the physical meaning of degradation mechanisms (e.g., the degradation path is monotonic). Parametric models, such as the Arrhenius model, are used for modeling the relationship between the degradation and the accelerating variable, allowing for extrapolation to the use conditio...
TL;DR: In this article, the authors used multiple predictor variables with a linear regression model to forecast economic data in economic data analysis, where the predicted values are calculated from a fitted linear regression models.
Abstract: Forecasting in economic data analysis is dominated by linear prediction methods where the predicted values are calculated from a fitted linear regression model. With multiple predictor variables, m...
TL;DR: In this paper, a new general methodology for constructing nonparametric and semiparametric Asymptotically Distribution-Free (ADF) tests for semi-parametric hypotheses in regression models for possibly dependent data coming from a strictly stationary process is proposed.
Abstract: This article proposes a new general methodology for constructing nonparametric and semiparametric Asymptotically Distribution-Free (ADF) tests for semiparametric hypotheses in regression models for possibly dependent data coming from a strictly stationary process. Classical tests based on the difference between the estimated distributions of the restricted and unrestricted regression errors are not ADF. In this article, we introduce a novel transformation of this difference that leads to ADF tests with well-known critical values. The general methodology is illustrated with applications to testing for parametric models against nonparametric or semiparametric alternatives, and semiparametric constrained mean–variance models. Several Monte Carlo studies and an empirical application show that the finite sample performance of the proposed tests is satisfactory in moderate sample sizes.
TL;DR: A hybrid method including nonparametric kernel-based method, least absolute deviations, and cross-validation method is suggested, which allows estimating parameters of the model and results indicate that the proposed method is potentially effective for predicting fuzzy time series data in real applications.
Abstract: This paper proposes a semiparametric autoregressive integrated moving average model for those real-world applications whose observed data are reported by fuzzy numbers. To this end, a hybrid method including nonparametric kernel-based method, least absolute deviations, and cross-validation method is suggested, which allows estimating parameters of the model including the autoregressive order $p$ , optimal value of the smoothing parameter $h$ , and fuzzy smooth function of the innovations, simultaneously. A correlation concept is also developed for fuzzy time series data and its main properties are investigated. Some common goodness-of-fit criteria are employed to examine the performance of the proposed fuzzy semiparametric time series model. A potential application of the proposed method is represented through simulated fuzzy time series data. To illustrate utility of this approach, it is applied to a set of real-life house price data in fuzzy environment. The results indicate that the proposed method is potentially effective for predicting fuzzy time series data in real applications.
TL;DR: In this paper, the authors compare the performance of the logit-mixed logit (LML) model and a mixed multinomial logit with normal heterogeneity (MMNL-N) model.
Abstract: The logit-mixed logit (LML) model is a very recent advancement in semiparametric discrete choice models. LML represents the mixing distribution of a logit kernel as a sieve function (polynomials, step functions, and splines, among many other variants). In the first part of this paper, we conduct Monte-Carlo studies to analyze the number of required parameters (e.g., polynomial order) in three LML variants to recover the true population distributions, and also compare the performance (in terms of accuracy, precision, estimation time, and model fit) of LML and a mixed multinomial logit with normal heterogeneity (MMNL-N). Our results indicate that adding too many parameters in LML may not be the best strategy to retrieve underlying taste heterogeneity; in fact, overspecified models generally perform worst in terms of BIC. We recommend to use neither minimum-BIC nor the most flexible specification, but we rather suggest to start with the same number of parameters as a parametric model (such as MMNL-N) while checking changes in the derived histogram of the mixing distribution. As expected, LML was able to recover bimodal-normal, lognormal, and uniform distributions much better than the misspecified MMNL-N. Computational efficiency makes LML advantageous in the process of searching for the final specification. In the second part of the paper, we estimate the willingness-to-pay (WTP) estimates of German consumers for different vehicle attributes when making alternative-fuel-car purchase choices. LML was able to capture the bimodal nature of WTP for vehicle attributes, which was not possible to retrieve using standard parametric specifications.
Abstract: We consider a model with both a parametric global trend and a nonparametric local trend. This model may be of interest in a number of applications in economics, finance, ecology, and geology. We first propose two hypothesis tests to detect whether two nested special cases are appropriate. For the case where both null hypotheses are rejected, we propose an estimation method to capture certain aspects of the time trend. We establish consistency and some distribution theory in the presence of a large sample. Moreover, we examine the proposed hypothesis tests and estimation methods through both simulated and real data examples. Finally, we discuss some potential extensions and issues when modelling time effects.
TL;DR: In this paper, a new class of semiparametric mixture of regression models, where the mixing proportions and variances are constants, but the component regression functions are smooth functions of a covariate, was proposed and two EM-type algorithms were proposed to achieve the optimal convergence rate for both the global parameters and the nonparametric regression functions.
Abstract: In this article, we propose and study a new class of semiparametric mixture of regression models, where the mixing proportions and variances are constants, but the component regression functions are smooth functions of a covariate. A one-step backfitting estimate and two EM-type algorithms have been proposed to achieve the optimal convergence rate for both the global parameters and the nonparametric regression functions. We derive the asymptotic property of the proposed estimates and show that both the proposed EM-type algorithms preserve the asymptotic ascent property. A generalized likelihood ratio test is proposed for semiparametric inferences. We prove that the test follows an asymptotic $$\chi ^2$$
-distribution under the null hypothesis, which is independent of the nuisance parameters. A simulation study and two real data examples have been conducted to demonstrate the finite sample performance of the proposed model.
TL;DR: A novel semiparametric HMM is considered, which comprises a semIParametric latent variable model to investigate the complex interrelationships among latent variables and a nonparametric transition model to examine the linear and nonlinear effects of potential predictors on hidden transition.
Abstract: In psychological, social, behavioral, and medical studies, hidden Markov models (HMMs) have been extensively applied to the simultaneous modeling of heterogeneous observation and hidden transition in the analysis of longitudinal data. However, the majority of the existing HMMs are developed in a parametric framework without latent variables. This study considers a novel semiparametric HMM, which comprises a semiparametric latent variable model to investigate the complex interrelationships among latent variables and a nonparametric transition model to examine the linear and nonlinear effects of potential predictors on hidden transition. The Bayesian P-splines approach and Markov chain Monte Carlo methods are developed to estimate the unknown, a Bayesian model comparison statistic, is employed to conduct model comparison. The empirical performance of the proposed methodology is evaluated through simulation studies. An application to a data set derived from the National Longitudinal Survey of Youth is presented.
TL;DR: In this article, the authors consider nonparametric multidimensional finite mixture models and propose a cross-validation-like procedure to select the partition in a finite horizon, where the conditional distributions are projected on step functions associated to some partition.
Abstract: In this paper, we consider nonparametric multidimensional finite mixture models and we are interested in the semiparametric estimation of the population weights. Here, the i.i.d. observations are assumed to have at least three components which are independent given the population. We approximate the semiparametric model by projecting the conditional distributions on step functions associated to some partition. Our first main result is that if we refine the partition slowly enough, the associated sequence of maximum likelihood estimators of the weights is asymptotically efficient, and the posterior distribution of the weights, when using a Bayesian procedure, satisfies a semiparametric Bernstein von Mises theorem. We then propose a cross-validation like procedure to select the partition in a finite horizon. Our second main result is that the proposed procedure satisfies an oracle inequality. Numerical experiments on simulated data illustrate our theoretical results.
TL;DR: In this paper, the authors consider a semiparametric model where the response variable following a transformation can be expressed by means of a regression model, and the form of the transformation is specified analytically up to an unknown transformation parameter.
Abstract: We consider a semiparametric model whereby the response variable following a transformation can be expressed by means of a regression model. In this model, the form of the transformation is specified analytically (up to an unknown transformation parameter), while the regression function is completely unknown. We develop testing procedures for the null hypothesis that this semiparametric model adequately describes the data at hand. In doing so, the test statistic is formulated on the basis of Fourier-type conditional expectations, an idea first put forward by Bierens (J Econom 20:105–134, 1982). The asymptotic distribution of the test statistic is obtained under the null as well as under alternative hypotheses. Since the limit null distribution is nonstandard, a bootstrap version is utilized in order to actually carry out the test procedure. Monte Carlo results are included that illustrate the finite-sample properties of the new method.
TL;DR: In this paper, a normal semiparametric mixture regression model is proposed for longitudinal data, which contains one smooth term and a set of possible linear predictors, and model terms are estimated using the penalized likelihood method with the EM algorithm.
Abstract: A normal semiparametric mixture regression model is proposed for longitudinal data. The proposed model contains one smooth term and a set of possible linear predictors. Model terms are estimated using the penalized likelihood method with the EM algorithm. A computationally feasible alternative method that provides an approximate solution is also introduced. Simulation experiments and a real data example are used to illustrate the methods.
TL;DR: This work proposes a semiparametric model, incorporating both knowledge and uncertainty about the true model, which is used to classify patients into treatment-favorable and nonfavorable subgroups in clinical trials.
Abstract: In analyzing clinical trials, one important objective is to classify the patients into treatment-favorable and nonfavorable subgroups. Existing parametric methods are not robust, and the commonly used classification rules ignore the fact that the implications of treatment-favorable and nonfavorable subgroups can be different. To address these issues, we propose a semiparametric model, incorporating both our knowledge and uncertainty about the true model. The Wald statistics is used to test the existence of subgroups, while the Neyman-Pearson rule to classify each subject. Asymptotic properties are derived, simulation studies are conducted to evaluate the performance of the method, and then method is used to analyze a real-world trial data.
01 Jan 2018
TL;DR: A critical review of parametric and semiparametric spatial econometric approaches focuses on the capability of each class of models to fit the main features of spatial data, leaving aside the technicalities related to the estimation methods.
Abstract: In this Chapter we provide a critical review of parametric and semiparametric spatial econometric approaches. We focus on the capability of each class of models to fit the main features of spatial data (such as strong and weak cross-sectional dependence, spatial heterogeneity, nonlinearities, and time persistence), leaving aside the technicalities related to the estimation methods. We also provide a brief discussion of the existent software developed to estimate most of the econometric models exposed in this Chapter.
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TL;DR: In this article, the authors considered sufficient conditions for identification of marginal structural models (MSMs), a general class of counterfactual models for the joint effects of time-varying treatment regimes in complex longitudinal studies subject to time varying confounding, when sequential randomization fails to hold due to unmeasured confounding.
Abstract: Robins (1998) introduced marginal structural models (MSMs), a general class of counterfactual models for the joint effects of time-varying treatment regimes in complex longitudinal studies subject to time-varying confounding He established identification of MSM parameters under a sequential randomization assumption (SRA), which essentially rules out unmeasured confounding of treatment assignment over time In this technical report, we consider sufficient conditions for identification of MSM parameters with the aid of a time-varying instrumental variable, when sequential randomization fails to hold due to unmeasured confounding Our identification conditions essentially require that no unobserved confounder predicts compliance type for the time-varying treatment, the longitudinal generalization of the identifying condition of Wang and Tchetgen Tchetgen (2018) Under this assumption, We derive a large class of semiparametric estimators that extends standard inverse-probability weighting (IPW), the most popular approach for estimating MSMs under SRA, by incorporating the time-varying IV through a modified set of weights The set of influence functions for MSM parameters is derived under a semiparametric model with sole restriction on observed data distribution given by the MSM, and is shown to provide a rich class of multiply robust estimators, including a local semiparametric efficient estimator
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TL;DR: In this article, the authors extended the joint Value at Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2017) via incorporating a realized measure, to drive the tail risk dynamics, as a potentially more efficient driver than daily returns.
Abstract: The joint Value at Risk (VaR) and expected shortfall (ES) quantile regression model of Taylor (2017) is extended via incorporating a realized measure, to drive the tail risk dynamics, as a potentially more efficient driver than daily returns. Both a maximum likelihood and an adaptive Bayesian Markov Chain Monte Carlo method are employed for estimation, whose properties are assessed and compared via a simulation study; results favour the Bayesian approach, which is subsequently employed in a forecasting study of seven market indices and two individual assets. The proposed models are compared to a range of parametric, non-parametric and semi-parametric models, including GARCH, Realized-GARCH and the joint VaR and ES quantile regression models in Taylor (2017). The comparison is in terms of accuracy of one-day-ahead Value-at-Risk and Expected Shortfall forecasts, over a long forecast sample period that includes the global financial crisis in 2007-2008. The results favor the proposed models incorporating a realized measure, especially when employing the sub-sampled Realized Variance and the sub-sampled Realized Range.
TL;DR: This study proposes semiparametric models for analysis of hierarchical count data containing excess zeros and overdispersion simultaneously and develops an EM algorithm based on Newton–Raphson equations for maximum penalized likelihood estimation approach.
Abstract: This study proposes semiparametric models for analysis of hierarchical count data containing excess zeros and overdispersion simultaneously. The methods discussed in this paper handle nonlinear covariate effects through flexible semiparametric multilevel regression techniques. This is performed by providing a comprehensive comparison of semiparametric multilevel zero-inflated negative binomial and semiparametric multilevel zero-inflated generalized Poisson models under the real and simulated data. An EM algorithm based on Newton-Raphson equations for maximum penalized likelihood estimation approach is developed. The performance of the proposed models is assessed by using a Monte Carlo simulation study. We also illustrated the methods by the analysis of decayed, missing, and filled teeth of children aged 5-14 years old.
TL;DR: This paper proposes a model selection procedure that simultaneously selects fixed and random effects using a maximum penalized likelihood method with the adaptive least absolute shrinkage and selection operator penalty to determine the correlation structure among multiple outcomes.
Abstract: Variable selection in semiparametric mixed models for longitudinal data remains a challenge, especially in the presence of multiple correlated outcomes. In this paper, we propose a model selection procedure that simultaneously selects fixed and random effects using a maximum penalized likelihood method with the adaptive least absolute shrinkage and selection operator penalty. Through random effects selection, we determine the correlation structure among multiple outcomes and therefore address whether a joint model is necessary. Additionally, we include a bivariate nonparametric component, as approximated by tensor product splines, to accommodate the joint nonlinear effects of two independent variables. We use an adaptive group least absolute shrinkage and selection operator to determine whether the bivariate nonparametric component can be reduced to additive components. To implement the selection and estimation method, we develop a two-stage expectation-maximization procedure. The operating characteristics of the proposed method are assessed through simulation studies. Finally, the method is illustrated in a clinical study of blood pressure development in children.
01 Sep 2018
TL;DR: In this article, the authors provide a new look at the classical estimation theory based on a geometrical Hilbert space-based approach and propose a semiparametric version of the Cramer- Rao Bound for the estimation of the finite-dimensional vector of the parameters of interest.
Abstract: This paper aims at providing a fresh look at semiparametric estimation theory and, in particular, at the Semiparametric Cramer-Rao Bound (SCRB). Semiparametric models are characterized by a finite-dimensional parameter vector of interest and by an infinite-dimensional nuisance function that is often related to an unspecified functional form of the density of the noise underlying the observations. We summarize the main motivations and the intuitive concepts about semi parametric models. Then we provide a new look at the classical estimation theory based on a geometrical Hilbert space-based approach. Finally, the semiparametric version of the Cramer- Rao Bound for the estimation of the finite-dimensional vector of the parameters of interest is provided.
TL;DR: A functional linear regression model for using functional (or imaging) predictors to predict clinical outcomes (e.g., disease status) while addressing missing clinical outcomes is proposed, and an exponential tilting semiparametric model is introduced to account for the nonignorable missing data mechanism.
Abstract: As an important part of modern health care, medical imaging data, which can be regarded as densely sampled functional data, have been widely used for diagnosis, screening, treatment, and prognosis, such as finding breast cancer through mammograms. The aim of this paper is to propose a functional linear regression model for using functional (or imaging) predictors to predict clinical outcomes (e.g., disease status), while addressing missing clinical outcomes. We introduce an exponential tilting semiparametric model to account for the nonignorable missing data mechanism. We develop a set of estimating equations and its associated computational methods for both parameter estimation and the selection of the tuning parameters. We also propose a bootstrap resampling procedure for carrying out statistical inference. Under some regularity conditions, we systematically establish the asymptotic properties (e.g., consistency and convergence rate) of the estimates calculated from the proposed estimating equations. Simulation studies and a real data analysis are used to illustrate the finite sample performance of the proposed methods.