Candidate: Asheber Abebe

Degree of: Doctor of Philosophy

Department: Statistics

Title: Nonlinear Regression Based on Ranks

Committee:
Dr. Joseph McKean, Chair
Dr. Daniel Mihalko
Dr. Gerald Sievers
Dr. Joshua Naranjo
Dr. Bradley Huitema

Date: Thursday, April 24, 2002, 4:00 p.m. – 6:00 p.m.
Alavi Commons Room, 6th floor Everett Tower

Abstract: This study presents robust methods for estimating parameters of nonlinear regression models. The proposed methods obtain estimates by minimizing rank-based dispersions instead of the
Euclidean norm. We focus on the Wilcoxon and generalized signed-rank dispersion functions. Asymptotic properties of the estimators are established under mild regularity conditions similar to those used in
least squares and least absolute deviations estimation. The study also shows that by considering the generalized signed-rank dispersion we obtain a class of estimators that encompasses most of the existing popular nonlinear regression estimators. As in linear models, these rank-based procedures provide estimators that are highly efficient. This fact is further confirmed for finite samples via a simulation study. Examples illustrating the robustness of the procedure are presented.

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