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Semiparametric Maximum Likelihood Estimation in Parametric Regression with Missing Covariates

Zhang, Zhiwei (2003) Semiparametric Maximum Likelihood Estimation in Parametric Regression with Missing Covariates. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

Parametric regression models are widely used in public health sciences. This dissertation is concerned with statistical inference under such models with some covariates missing at random. Under natural conditions, parameters remain identifiable from the observed (reduced) data. If the always observed covariates are discrete or can be discretized, we propose a semiparametric maximum likelihood method which requires no parametric specification of the selection mechanism or the covariate distribution. Simple conditions are given under which the semiparametric maximum likelihood estimator (MLE) exists. For ease of computation, we also consider a restricted MLE which maximizes the likelihood over covariate distributions supported by the observed values. The two MLEs are asymptotically equivalent and strongly consistent for a class of topologies on the parameter set. Upon normalization, they converge weakly to a zero-mean Gaussian process in a suitable space. The MLE of the regression parameter, in particular, achieves the semiparametric information bound, which can be consistently estimated by perturbing the profile log-likelihood. Furthermore, the profile likelihood ratio statistic is asymptotically chi-squared. An EM algorithm is proposed for computing the restricted MLE and for variance estimation. Simulation results suggest that the proposed method performs resonably well in moderate-sized samples. In contrast, the analogous parametric maximum likelihood method is subject to severe bias under model misspecification, even in large samples. The proposed method can be applied to related statistical problems.


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Details

Item Type: University of Pittsburgh ETD
Status: Unpublished
Creators/Authors:
CreatorsEmailPitt UsernameORCID
Zhang, Zhiweizhzst5@pitt.eduZHZST5
ETD Committee:
TitleMemberEmail AddressPitt UsernameORCID
Committee ChairRockette, Howard E herbst@pitt.eduHERBST
Committee MemberTang, Gonggot1@pitt.eduGOT1
Committee MemberChang, Joyce Hchangjh@upmc.edu
Committee MemberMazumdar, Satimaz1@pitt.eduMAZ1
Committee MemberAnderson, Stewart Jsja@nsabp.pitt.eduSJA
Date: 12 December 2003
Date Type: Completion
Defense Date: 19 November 2003
Approval Date: 12 December 2003
Submission Date: 24 November 2003
Access Restriction: No restriction; Release the ETD for access worldwide immediately.
Institution: University of Pittsburgh
Schools and Programs: Graduate School of Public Health > Biostatistics
Degree: PhD - Doctor of Philosophy
Thesis Type: Doctoral Dissertation
Refereed: Yes
Uncontrolled Keywords: Aymptotic normality; Consistency; EM algorithm; Infinite-dimensional M-estimation; Missing at random; Profile likelihood; Semiparametric likelihood; Missing covariates; Parametric regression
Other ID: http://etd.library.pitt.edu/ETD/available/etd-11242003-205144/, etd-11242003-205144
Date Deposited: 10 Nov 2011 20:06
Last Modified: 15 Nov 2016 13:52
URI: http://d-scholarship.pitt.edu/id/eprint/9785

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