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Generalized Minimum Penalized Hellinger Distance Estimation and Generalized Penalized Hellinger Deviance Testing for Generalized Linear Models: The Discrete Case

In this dissertation, robust and efficient alternatives to quasi-likelihood estimation and likelihood ratio tests are developed for discrete generalized linear models. The estimation method considered is a penalized minimum Hellinger distance procedure that generalizes a procedure developed by Harris and Basu for estimating parameters of a single discrete probability distribution from a random sample. A bootstrap algorithm is proposed to select the weight of the penalty term. Simulations are carried out to compare the new estimators with quasi-likelihood estimation. The robustness of the estimation procedure is demonstrated by simulation work and by Hapel's α-influence curve. Penalized minimum Hellinger deviance tests for goodness-of-fit and for testing nested linear hypotheses are proposed and simulated. A nonparametric bootstrap algorithm is proposed to obtain critical values for the testing procedure.

Identiferoai:union.ndltd.org:UTAHS/oai:digitalcommons.usu.edu:etd-8174
Date01 May 2001
CreatorsYan, Huey
PublisherDigitalCommons@USU
Source SetsUtah State University
Detected LanguageEnglish
Typetext
Formatapplication/pdf
SourceAll Graduate Theses and Dissertations
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