Showing papers on "Semiparametric model published in 1997"
TL;DR: In this paper, a Kolmogorov-Smirnov-type statistic was proposed to test the validity of the logistic link function in a case-control sampling plan.
Abstract: SUMMARY We test the logistic regression assumption under a case-control sampling plan. After reparameterisation, the assumed logistic regression model is equivalent to a two-sample semiparametric model in which the log ratio of two density functions is linear in data. By identifying this model with a biased sampling model, we propose a Kolmogorov-Smirnovtype statistic to test the validity of the logistic link function. Moreover, we point out that this test statistic can also be used in mixture sampling. We present a bootstrap procedure along with some results on simulation and on analysis of two real datasets.
248 citations
TL;DR: The authors examines alternative semi-parametric quasi-likelihood approaches, which embed sample versions of the moment conditions used in Generalized Method of Moments (GMM) in a nonparametric likelihood function by use of additional parameters associated with these moment conditions.
Abstract: Since Hansen's (1982) seminal paper, the generalised method of moments (GMM) has become an increasingly important method for estimation and inference in econometrics. This paper examines alternative semi-parametric quasi-likelihood approaches. Essentially, these methods embed sample versions of the moment conditions used in GMM in a non-parametric quasi-likelihood function by use of additional parameters associated with these moment conditions. Specification and misspecification tests may be defined which are similar in nature to the classical tests and are first-order equivalent to the corresponding GMM statistics. The structure of the semi-parametric quasi-maximum likelihood estimator is explored for models estimated by instrumental variables.
244 citations
TL;DR: In this paper, the authors investigated the potential of Bayes methods for the analysis of survival data using semiparametric models based on either the hazard or the intensity function, where the nonparametric part of every model is assumed to be a realization of a stochastic process.
Abstract: This review article investigates the potential of Bayes methods for the analysis of survival data using semiparametric models based on either the hazard or the intensity function. The nonparametric part of every model is assumed to be a realization of a stochastic process. The parametric part, which may include a regression parameter or a parameter quantifying the heterogeneity of a population, is assumed to have a prior distribution with possibly unknown hyperparameters. Careful applications of some recently popular computational tools, including sampling-based algorithms, are used to find posterior estimates of several quantities of interest even when dealing with complex models and unusual data structures. The methodologies developed herein are motivated and aimed at analyzing some common types of survival data from different medical studies; here we focus on univariate survival data in the presence of fixed and time-dependent covariates, multiple event-time data for repeated nonfatal events, ...
195 citations
TL;DR: In this paper, the authors show that the limiting distribution arises naturally when one uses an efficient test statistic to test a single parameter in a semiparametric or parametric model.
Abstract: Authors have shown that the time-sequential joint distributions of many statistics used to analyze data arising from group-sequential time-to-event and longitudinal studies are multivariate normal with an independent increments covariance structure. In Theorem 1 of this article, we demonstrate that this limiting distribution arises naturally when one uses an efficient test statistic to test a single parameter in a semiparametric or parametric model. Because we are able to think of many of the statistics in the literature in this fashion, the limiting distribution under investigation is just a special case of Theorem 1. Using this general structure, we then develop an information-based design and monitoring procedure that can be applied to any type of model for any type of group-sequential study provided that there is a unique parameter of interest that can be efficiently tested.
151 citations
TL;DR: In this article, the authors obtain a LAN result under quite natural and economical conditions for many time-series models, and construct adaptive estimators for (part of) the Euclidean parameter in these models.
Abstract: In a framework particularly suited for many time-series models we obtain a LAN result under quite natural and economical conditions. This enables us to construct adaptive estimators for (part of) the Euclidean parameter in these semiparametric models. Special attention is directed to group models in time series with the important subclass of models with time varying location and scale. Our set-up is confronted with the existing literature and, as examples, we reconsider linear regression and ARMA, TAR and ARCH models.
119 citations
TL;DR: In this paper, the nonparametric version of the classical mixed model is considered and the common hypotheses of (parametric) main effects and interactions are reformulated in a non-parametric setup.
118 citations
TL;DR: In this paper, a Markov-chain Monte Carlo (MCMC) method is developed to compute the features of the posterior distribution of a log-linear model, and a model selection method for obtaining a more parsimonious set of predictors is studied.
Abstract: Bayesian semiparametric inference is considered for a loglinear model. This model consists of a parametric component for the regression coefficients and a nonparametric component for the unknown error distribution. Bayesian analysis is studied for the case of a parametric prior on the regression coefficients and a mixture-of-Dirichlet-processes prior on the unknown error distribution. A Markov-chain Monte Carlo (MCMC) method is developed to compute the features of the posterior distribution. A model selection method for obtaining a more parsimonious set of predictors is studied. The method adds indicator variables to the regression equation. The set of indicator variables represents all the possible subsets to be considered. A MCMC method is developed to search stochastically for the best subset. These procedures are applied to two examples, one with censored data.
115 citations
TL;DR: In this article, a nonparametric model passing through the true model is constructed and the score for the parametric model is estimated nonparametrically and the estimator is shown to be √ n consistent and asymptotically normal.
Abstract: This paper presents a procedure for analyzing a model in which the parameter vector has two parts: a finite-dimensional component 8 and a nonparametric component A. The procedure does not require parametric modeling of λ but assumes that the true density of the data satisfies an index restriction. The idea is to construct a parametric model passing through the true model and to estimate θ by setting the score for the parametric model to zero. The score is estimated nonparametrically and the estimator is shown to be √N consistent and asymptotically normal. The estimator is then shown to attain the semiparametric efficiency bound characterized in Begun et al. (1983) for multivariate nonlinear regression, simultaneous equations, partially specified regression, index regression, censored regression, switching regression, and disequilibrium models in which the error densities are unknown.
113 citations
TL;DR: In this paper, the authors construct adaptive estimators in a general GARCH in mean-type context including integrated GARCH models, based on a general LAN theorem for time-series models.
108 citations
TL;DR: In this paper, a nonparametric model for the unknown joint distribution for the missing data, the observed covariates and the proxy is proposed, which defines the measurement error component of the model which relates the missing covariates X with a proxy W.
Abstract: SUMMARY We develop a model and a numerical estimation scheme for a Bayesian approach to inference in case-control studies with errors in covariables. The model proposed in this paper is based on a nonparametric model for the unknown joint distribution for the missing data, the observed covariates and the proxy. This nonparametric distribution defines the measurement error component of the model which relates the missing covariates X with a proxy W. The oxymoron 'nonparametric Bayes' refers to a class of flexible mixture distributions. For the likelihood of disease, given covariates, we choose a logistic regression model. By using a parametric disease model and nonparametric exposure model we obtain robust, interpretable results quantifying the effect of exposure.
89 citations
TL;DR: In this article, the structure of estimating functions based on the dual differential geometry of statistical inference and its extension to fibre bundles is discussed. And the concept of m-curvature freeness plays a fundamental role in solving the above problems.
Abstract: For semi-parametric statistical estimation, when an estimating function exists, it often provides an efficient or a good consistent estimator of the parameter of interest against nuisance parameters of infinite dimensions. The present paper elucidates the structure of estimating functions, based on the dual differential geometry of statistical inference and its extension to fibre bundles. The paper studies the following problems. First, when does an estimating function exist and what is the set of all the estimating functions? Second, how are the asymptotic variances of the estimators derived from estimating functions and when are the estimators efficient? Third, how do we adaptively choose a practically good (quasi-)estimating function from the observed data? The concept of m-curvature freeness plays a fundamental role in solving the above problems.
TL;DR: In this article, the authors present a family of tests based on correlated random effects models which provide a synthesis and a generalization of recent work on homogeneity testing, and derive the general form of the score statistic for testing that the random effects have a variance equal to 0.
Abstract: SUMMARY We present a family of tests based on correlated random effects models which provides a synthesis and a generalization of recent work on homogeneity testing. In these models each subject has a particular random effect, but the random effects between subjects are correlated. We derive the general form of the score statistic for testing that the random effects have a variance equal to 0. We apply this result to both parametric and semiparametric models. In both cases we show that under certain conditions the score statistic has an asymptotic normal distribution. We consider several applications of this theory, including overdispersion, heterogeneity between groups, spatial correlations and genetic linkage.
TL;DR: In this paper, the authors give an introduction to the theory and application of multivariate and semiparametric kernel smoothing using local polynomial fitting which includes the Nadaraya-Watson estimator.
Abstract: The paper gives an introduction to theory and application of multivariate and semiparametric kernel smoothing. Multivariate nonparametric density estimation is an often used pilot tool for examining the structure of data. Regression smoothing helps in investigating the association between covariates and responses. We concentrate on kernel smoothing using local polynomial fitting which includes the Nadaraya-Watson estimator. Some theory on the asymptotic behavior and bandwidth selection is provided. In the applications of the kernel technique, we focus on the semiparametric paradigm. In more detail we describe the single index model (SIM) and the generalized partial linear model (GPLM).
TL;DR: In this article, a simple semiparametric estimator of the moments of the density function of the latent variable's unobserved random component is proposed. But the results can be used as starting values for parametric estimators, for specification testing including tests of latent error skewness and kurtosis, and to estimate coefficients of discrete explanatory variables in the model.
Abstract: Latent variable discrete choice model estimation and interpretation depend on the density function of the latent variable's unobserved random component. This paper provides a simple semiparametric estimator of the moments of this density. The results can be used as starting values for parametric estimators, to estimate the appropriate location and scaling for semiparametric estimators, for specification testing including tests of latent error skewness and kurtosis, and to estimate coefficients of discrete explanatory variables in the model.
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TL;DR: An improved AIC-based criterion for model selection in general smoothing-based models, including semiparametric models and additive models, is derived in this paper, where examples are provided of applications to goodness-of-fit, smoothing parameter and variable selection in an additive model and in a model with a nonlinear function of linear terms.
Abstract: An improved AIC-based criterion is derived for model selection in general smoothing-basedmodeling, including semiparametric models and additive models. Examples areprovided of applications to goodness-of-fit, smoothing parameter and variable selectionin an additive model and semiparametric models, and variable selection in a model witha nonlinear function of linear terms.
TL;DR: In this article, a nonparametric test of constant variance for the errors in a linear model is constructed through non-parametric smoothing of the residuals on a suitably transformed scale.
TL;DR: In this article, a general approach to semiparametric regression model construction using the notation of a transfer functional is proposed, which generalizes the estimators of the parameters of the proportional hazards and the additive risk models.
Abstract: SUMMARY A general approach to semiparametric regression model construction is proposed, using the notation of a transfer functional. Estimators of unknown regression parameters are proposed, generalising the estimators of the parameters of the proportional hazards and the additive risk models.
TL;DR: In this paper, the finite sample properties of three semiparametric estimators, several versions of the modified rescaled range, MRR, and three versions of GHURST estimator are investigated.
Abstract: The finite sample properties of three semiparametric estimators, several versions of the modified rescaled range, MRR, and three versions of the GHURST estimator are investigated. Their power and size for testing for long memory under short-run effects, joint short and long-run effects, heteroscedasticity andt-distributions are given using Monte Carlo methods.
TL;DR: A semiparametric regression model is proposed, extending the fully parametric model of Thall (1988, Biometrics 44, 197-209), to estimate and test for covariate effects on the rate of events over time while also accounting for the possibly time-varying nature of the underlying event rate.
Abstract: This paper deals with analysis of data from longitudinal studies where the rate of a recurrent event characterizing morbidity is the primary criterion for treatment evaluation. We consider clinical trials which require patients to visit their clinical center at successive scheduled times as part of follow-up. At each visit, the patient reports the number of events that occurred since the previous visit, or an examination reveals the number of accumulated events, such as skin cancers. The exact occurrence times of the events are unavailable and the actual patient visit times typically vary randomly about the scheduled follow-up times. Each patient's record thus consists of a sequence of clinic visit dates, event counts corresponding to the successive time intervals between clinic visits, and baseline covariates. We propose a semiparametric regression model, extending the fully parametric model of Thall (1988, Biometrics 44, 197-209), to estimate and test for covariate effects on the rate of events over time while also accounting for the possibly time-varying nature of the underlying event rate. Covariate effects enter the model parametrically, while the underlying time-varying event rate is modelled nonparametrically. The method of Severini and Wong (1992, Annals of Statistics 20, 1768-1802) is used to construct asymptotically efficient estimators of the parametric component and to specify their asymptotic distribution. A simulation study and application to a data set are provided.
TL;DR: In this paper, an adaptive parametric test statistic is constructed and a large sample study for this adaptive parameteretric test statistics is presented, where the design points (xi,ti) are known and nonrandom and the ei are iid random errors with Ee1 = 0 and Ee2 1 = α2<∞.
Abstract: Consider the semiparametric regression model Yi = x′iβ +g(ti)+ei for i=1,2, …,n. Here the design points (xi,ti) are known and nonrandom and the ei are iid random errors with Ee1 = 0 and Ee2 1 = α2<∞. Based on g(.) approximated by a B-spline function, we consider using atest statistic for testing H0 : β = 0. Meanwhile, an adaptive parametric test statistic is constructed and a large sample study for this adaptive parametric test statistic is presented.
TL;DR: Spline smoothing is extended in this paper to express prior knowledge about general features of the curve in the form of a linear differential operator that annihilates a specified parametric model for the data.
Abstract: Nonparametric regression techniques, which estimate functions directly from noisy data rather than relying on specific parametric models, now play a central role in statistical analysis. We can improve the efficiency and other aspects of a nonparametric curve estimate by using prior knowledge about general features of the curve in the smoothing process. Spline smoothing is extended in this paper to express this prior knowledge in the form of a linear differential operator that annihilates a specified parametric model for the data. Roughness in the fitted function is defined in terms of the integrated square of this operator applied to the fitted function. A fastO(n) algorithm is outlined for this smart smoothing process. Illustrations are provided of where this technique proves useful.
TL;DR: In this paper, the authors proposed a test of semiparametric versus parametric single index modeling, which is proved to be rate-optimal in the sense that it provides (rate) minimal distance between hypothesis and alternative for a given power function.
Abstract: Discrete choice models are frequently used in statistical and econometric practice. Standard models such as logit models are based on exact knowledge of the form of the link and linear index function. Semiparametric models avoid possible misspecification but often introduce a computational burden especially when optimization over nonparametric and parametric components are to be done iteratively. It is therefore interesting to decide between approaches. Here we propose a test of semiparametric versus parametric single index modelling. Our procedure allows the (linear) index of the semiparametric alternative to be different from that of the parametric hypothesis. The test is proved to be rate-optimal in the sense that it provides (rate) minimal distance between hypothesis and alternative for a given power function.
TL;DR: In this paper, the Type-3 Tobit model with weak restrictions on the distribution of the error terms and regressors is considered, and two least squares-type estimation approaches are proposed under the condition that the error term and regressor are independent.
01 Jan 1997
TL;DR: Le Cam & Yang as discussed by the authors addressed the following question: given observations X (n) = (X 1n, X 2 n, X n, etc, Xnn) distributed according to P θ(n) ; θ∈R k, where R k is the number of observations.
Abstract: Le Cam & Yang (1988) addressed broadly the following question: Given observations X (n) = (X1n,…, Xnn) distributed according to P θ (n) ; θ∈R k
TL;DR: In this article, the authors study the nonparametric estimation of the average growth curve under a very general parametric form of the covariance structure that allows for monotone transformation of the time scale.
TL;DR: In this article, instead of using exclusively a parametric or a nonparametric estimator, the authors propose to fit a weighted average of both the parametric and non-parametric estimates.
Abstract: One method for estimating the hazard function is to use a parametric estimator, provided that the underlying distribution of the data can be assumed to belong to some well known family of distributions depending on an unknown, possibly vector-valued parameter. Another approach is to use nonparametric estimators, such as Cox's proportional hazard models, kernel hazard estimators, and so on. However, nonparametric estimators are less efficient than suitably chosen parametric models. But, regardless of how suitable a parametric model may be, because of errors associated with data collection, it is impossible to determine with certainty whether the observed data are actually generated by the postulated model. Consequently, instead of using exclusively a parametric or a nonparametric estimator, we propose to fit a weighted average of both. The weight is estimated by minimizing the mean square error of the combination. The main point is that we expect the proposed model to assign more weight to the est...
TL;DR: In this paper, the goodness-of-fit test is applied to data from the Mayo Clinic trial in primary biliary cirrhosis of the liver and the test is suitable for practical use.
Abstract: SUMMARY Kolmogorov-Smirnov and Cramer-von Mises type test statistics based on the standardised cumulative hazard process are proposed. It is very difficult to evaluate their asymptotic distributions, but they can be approximated by the use of the bootstrap. The advantages of the goodness-of-fit test are that arbitrary partitions of the time axis and covariate spaces are not needed for evaluating test statistics and that it has excellent consistency properties. The test is applied to data from the Mayo Clinic trial in primary biliary cirrhosis of the liver. A simulation study indicates that the proposed test is suitable for practical use.
TL;DR: In this paper, the authors investigated the semiparametric efficiency of the conditional maximum likelihood estimation in some panel models, and showed that the nonparametric component of the model is the unknown distribution of the fixed effect, and the complete sufficient statistic does not depend on the parameter of interest.
Abstract: This paper investigates the semiparametric efficiency of the conditional maximum likelihood estimation in some panel models. The nonparametric component of the model is the unknown distribution of the fixed effect. For the exponential panel model, there exists a complete sufficient statistic for the fixed effect. When the complete sufficient statistic does not depend on the parameter of interest, the conditional maximum likelihood estimator (CMLE) achieves the semiparametric efficiency bound. In particular, the CMLE is semiparametrically efficient for the panel Poisson regression model and the panel negative binomial model.
TL;DR: In this article, asymptotical properties of estimators of regression parameters and baseline survival function arc are investigated in the case of one of considered classes, generalizing the proportional and additive hazards, proportional odds and other models.
Abstract: Classes of semiparametric models, generalizing the proportional and additive hazards, proportional odds and other models are considered. Asymptotical properties of estimators of regression parameters and baseline survival function arc investigated in the case of one of considered classes.