Date of Award:
Doctor of Philosophy (PhD)
Mathematics and Statistics
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.
Yan, Huey, "Generalized Minimum Penalized Hellinger Distance Estimation and Generalized Penalized Hellinger Deviance Testing for Generalized Linear Models: The Discrete Case" (2001). All Graduate Theses and Dissertations. 7066.
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