Date of Award

6-2004

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Dr. Joseph McKean

Second Advisor

Dr. Gerald Sievers

Third Advisor

Dr. Magdalena Bugaj

Fourth Advisor

Dr. Thomas Hettmansperger

Abstract

Affine equivariant estimates for the regression coefficient matrix of the multivariate linear model are proposed. These estimates are based on a transformation and retransformation technique that uses Tyler's (1987) M -estimator of scatter. The proposed estimates are obtained by retransforming the componentwiserank-based estimate due to Davis and McKean (1993) and a componentwise generalized rank estimate. Asymptotic properties of the estimates are established under some regularity conditions. It is shown that both estimates have a multivariate normal limiting distribution. The influence function of the retransformed generalized rank estimate has a bounded influence in both factor and response spaces. It is shown through a simulation study that the transformed-retransformed R and GR estimates are highly efficient compared to the non-equivariant componentwise R, GR and least absolute deviations estimates. Also, it is shown that the new estimates perform better than the least squares estimate when the errors have a heavy tailed distribution. Based on the new estimates quadratic procedures for testing the general hypothesis H0: [Special characters omitted.]

Access Setting

Dissertation-Open Access

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