HIGH DIMENSIONAL VARIABLE SELECTION VIA PENALIZED LIKELIHOOD FOR GENERALIZED LINEAR MODELS

Qi, Wenjing (2015) HIGH DIMENSIONAL VARIABLE SELECTION VIA PENALIZED LIKELIHOOD FOR GENERALIZED LINEAR MODELS. Doctoral Dissertation, University of Pittsburgh. (Unpublished)

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Abstract

Variable selection is fundamental to high dimensional statistical modeling. In this study, penalized likelihood methods are examined to simultaneously estimate parameters and select variables for generalized linear models. We focus on the variable selection and parameter estimation properties rather than the prediction properties of the estimators and are more interested in situations where the number of parameters diverges with the sample size. We prove the parameter estimation consistency of several widely used penalized likelihood estimators for generalized linear models. We define the relaxed sense and prove that it loosens the regularity and sparsity conditions of the parameter estimation and variable selection consistency. We propose a bootstrap method that can greatly improve the variable selection performances and reduce false discovery rates. We conduct simulation studies to compare the variable selection and parameter estimation properties of these penalized likelihood estimators for logistic models. We then illustrate our methods on gene expression data.

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Details

Item Type:	University of Pittsburgh ETD
Status:	Unpublished
Creators/Authors:	Creators Email Pitt Username ORCID Qi, Wenjing wq4@pitt.edu WQ4
ETD Committee:	Title Member Email Address Pitt Username ORCID Committee Chair Iyengar, Satish ssi@pitt.edu SSI Committee Member Gleser, Leon J. gleser@pitt.edu GLESER Committee Member Cheng, Yu yucheng@pitt.edu YUCHENG Committee Member Anderson, Stewart J. sja@pitt.edu SJA
Date:	14 January 2015
Date Type:	Publication
Defense Date:	25 August 2014
Approval Date:	14 January 2015
Submission Date:	3 December 2014
Access Restriction:	5 year -- Restrict access to University of Pittsburgh for a period of 5 years.
Number of Pages:	77
Institution:	University of Pittsburgh
Schools and Programs:	Dietrich School of Arts and Sciences > Statistics
Degree:	PhD - Doctor of Philosophy
Thesis Type:	Doctoral Dissertation
Refereed:	Yes
Uncontrolled Keywords:	Variable selection, High dimensionality, Penalized methods, Generalized linear models, Bootstrap method.
Date Deposited:	14 Jan 2015 15:38
Last Modified:	14 Jan 2020 06:15
URI:	http://d-scholarship.pitt.edu/id/eprint/23758

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