Date of Award

8-2003

Degree Name

Doctor of Philosophy

Department

Statistics

First Advisor

Dr. Joshua D. Naranjo

Second Advisor

Dr. Joseph McKean

Third Advisor

Dr. Gerald L. Sievers

Fourth Advisor

Dr. Bradley E. Huitema

Abstract

The main purpose of this dissertation is to obtain an estimate of the slope parameter in a regression model that is robust to outlying values in both the x - and Y-spaces. The least squares method, though known to be optimal for normal errors, can yield estimates with infinitely large MSE's if the error distribution is thick-tailed. Regular rank-based methods like the Wilcoxon method are known to be robust to outlying values in the Y -space, but it is still grossly affected by outlying values in x -space.

This dissertation derives an estimate of the slope from an estimating function that is essentially the Spearman correlation between the x values and the residuals. It is shown to be a special case of the GR estimates of Sievers (1983) in the context of simple linear regression. Thus, it is robust to outlying values in the x - and Y -spaces. Three proposed schemes are presented for obtaining multiple regression estimates. Two of these schemes, namely, the residual method and the bias adjustment method, are shown to yield estimates that are consistent.

Access Setting

Dissertation-Open Access

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