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Full-Text Articles in Statistics and Probability
Generalized Minimum Penalized Hellinger Distance Estimation And Generalized Penalized Hellinger Deviance Testing For Generalized Linear Models: The Discrete Case, Huey Yan
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
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 …
Selecting The Best Linear Model From A Subset Of All Possible Models For A Given Set Of Predictors In A Multiple Linear Regression Analysis, David L. Jensen
Selecting The Best Linear Model From A Subset Of All Possible Models For A Given Set Of Predictors In A Multiple Linear Regression Analysis, David L. Jensen
All Graduate Theses and Dissertations, Spring 1920 to Summer 2023
Sixteen "model building" and "model selection" procedures commonly encountered in industry, all of which were initially alleged to be capable of identifying the best model from the collection of 2k possible linear models corresponding to a given set of k predictors in a multiple linear regression analysis, were individually summarized and subsequently evaluated by considering their comparative advantages and limitations from both a theoretical and a practical standpoint. It was found that none of the proposed procedures were absolutely infallible and that several were actually unsuitable. However, it was also found that most of these techniques could still be …