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Semiparametric model
About: Semiparametric model is a research topic. Over the lifetime, 3297 publications have been published within this topic receiving 116743 citations.
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2,184 citations
TL;DR: In this article, empirical likelihood ratio statistics for various parameters of an unknown distribution have been used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods.
Abstract: For some time, so-called empirical likelihoods have been used heuristically for purposes of nonparametric estimation. Owen showed that empirical likelihood ratio statistics for various parameters $\theta(F)$ of an unknown distribution $F$ have limiting chi-square distributions and may be used to obtain tests or confidence intervals in a way that is completely analogous to that used with parametric likelihoods. Our objective in this paper is twofold: first, to link estimating functions or equations and empirical likelihood; second, to develop methods of combining information about parameters. We do this by assuming that information about $F$ and $\theta$ is available in the form of unbiased estimating functions. Empirical likelihoods for parameters are developed and shown to have properties similar to those for parametric likelihood. Efficiency results for estimates of both $\theta$ and $F$ are obtained. The methods are illustrated on several problems, and areas for future investigation are noted.
1,692 citations
TL;DR: In this article, the authors proposed a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on the vector of explanatory variables in the presence of missing response data.
Abstract: We propose a class of inverse probability of censoring weighted estimators for the parameters of models for the dependence of the mean of a vector of correlated response variables on a vector of explanatory variables in the presence of missing response data. The proposed estimators do not require full specification of the likelihood. They can be viewed as an extension of generalized estimating equations estimators that allow for the data to be missing at random but not missing completely at random. These estimators can be used to correct for dependent censoring and nonrandom noncompliance in randomized clinical trials studying the effect of a treatment on the evolution over time of the mean of a response variable. The likelihood-based parametric G-computation algorithm estimator may also be used to attempt to correct for dependent censoring and nonrandom noncompliance. But because of possible model misspecification, the parametric G-computation algorithm estimator, in contrast with the proposed w...
1,510 citations
Book•
01 Sep 1993
TL;DR: Asymptotic Inference for (Finite-Dimensional) Parametric Models as mentioned in this paper has been studied in the context of infinite-dimensional parametric models, where information bounds for Euclidean parameters in infinite-dimensional models have been derived.
Abstract: Introduction.- Asymptotic Inference for (Finite-Dimensional) Parametric Models.- Information Bounds for Euclidean Parameters in Infinite-Dimensional Models.- Euclidean Parameters: Further Examples.- Information Bounds for Infinite-Dimensional Parameters.- Infinite-Dimensional Parameters: Further Examples: Construction of Examples.
1,293 citations
TL;DR: In this article, the authors investigated the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions and proposed an estimator, obtained as a solution of a pseudo-likelihood equation, which is consistent, asymptotically normal and fully efficient at independence.
Abstract: SUMMARY This paper investigates the properties of a semiparametric method for estimating the dependence parameters in a family of multivariate distributions. The proposed estimator, obtained as a solution of a pseudo-likelihood equation, is shown to be consistent, asymptotically normal and fully efficient at independence. A natural estimator of its asymptotic variance is proved to be consistent. Comparisons are made with alternative semiparametric estimators in the special case of Clayton's model for association in bivariate data.
1,280 citations