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Doctoral Dissertation Announcement
Candidate: Kuanwong Watcharotone
Doctor of Philosophy
Title: On Robustification of Some Procedures Used in Analysis of Covariance
Dr. Joseph W. McKean, Chair
Dr. Jung Chao Wang
Dr. Bradley Huitema
Date: Friday, February 19, 2010 2:00 p.m. - 4:00 p.m.
6625 Everett Tower
This study discusses robust procedures for the analysis of covariance (ANCOVA) models. These methods are based on rank-based (R) fitting procedures, which are quite analogous to the traditional ANCOVA methods based on least squares fits. Initial empirical results show that the validity of R procedures is similar to the least squares procedures. In terms of power, there is a small loss in efficiency to least squares methods when the random errors have a normal distribution but the rank-based procedures are much more powerful for the heavy-tailed error distributions in this study.
Rank-based analogs are also developed for the pick-a-point, the adjusted means, and the Johnson-Neyman technique procedures. Instead of regions of nonsignificance, pick-a-point procedures obtain the confidence interval for treatment difference at any selected covariate point chosen. For the traditional adjusted means procedures, it is established that they can be derived from the underlying design by using the normal equations. This is then used to derive the rank-based adjusted means, showing that they have the desired asymptotic representation. The study compares these with their LS counterparts and naive adjusted Hodges-Lehmann and the adjusted medians. The robust procedures, which are weighted Wilcoxon and pseudo-observations, are used for the Johnson-Neyman technique to obtain the region of nonsignificance of the treatments. Examples are discussed. For each of these ANCOVA procedures, Monte Carlo analysis is conducted to compare empirically the differences of the traditional and robust methods. The results indicate that R estimates seem to have more power than the traditional least squares for longer-tailed distribution.