Reduction the distribution of maximum likelihood estimator in regression models (Master thesis)

Εβρένογλου, Θεόδωρος

The maximum likelihood method is the most widely used method for the pa- rameter estimation in regression models. This method owes its popularity to the desirable properties of the corresponding estimators in the presence of a large sample. However, when a large sample is not available the corresponding estimators are usually biased and the bias a ects signi cantly the nal results. The objective of this thesis is: a) to review some regression models for cate- gorical data such as logistic regression and Cox model for survival analysis, b) to review methods whose aim is bias reduction in parameter estimation for regression models. This thesis focuses on methods based on the Taylor expan- sion, for there is a plethora of references in the literature which are referred to the superiority of those methods. The main method which is presented in that thesis is the method proposed by Firth (1993). The modi ed bias-reduced esti- mator has some superior properties over the traditional maximum likelihood estimator. After describing the theoretical background of di erent methods for the bias reduction of the maximum likelihood estimator we applied Firth's method in two real datasets. In our analyses we used the statistical package of R. Finally, topics for further research are discussed.
Institution and School/Department of submitter: Πανεπιστήμιο Ιωαννίνων. Σχολή Θετικών Επιστημών. Τμήμα Μαθηματικών
Subject classification: Γραμμικά μοντέλα (Στατιστική)
Keywords: Εκτιμητής μέγιστης πιθανοφάνεις,Μεροληψία,Μικρά δείγματα,Σπάνια γεγονότα,Maximum likelihood estimation,Bias,Small samples,Rare events
Appears in Collections:Διατριβές Μεταπτυχιακής Έρευνας (Masters)

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