Abstract #300975

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JSM 2003 Abstract #300975
Activity Number: 93
Type: Contributed
Date/Time: Monday, August 4, 2003 : 8:30 AM to 10:20 AM
Sponsor: General Methodology
Abstract - #300975
Title: Optimal Critical Values of Pretests When Estimating the Regression Error Variance: Analytical Findings Under a General Loss Structure
Author(s): Alan T. Wan*+
Companies: City University of Hong Kong
Address: Dept. of Management Sciences, Kowloon, , , Hong Kong
Keywords: entropy loss ; first-order differentiable ; Lebesque integrable ; linear restrictions ; LINEX loss ; variance homogeneity
Abstract:

This paper revisits the problem of estimating the regression error variance after preliminary hypothesis tests for either linear restrictions on the coefficients or homogeneity of variances. There is an extensive literature that discusses this problem, particularly in terms of the sampling properties of the pretest estimators using various loss functions as a basis of analysis. In this paper, a unified framework for analyzing the risk properties of these estimators is developed under a general class of loss structures that incorporates virtually all first-order differentiable losses. Particular attention is given to the choice of critical values for the pretests. Analytical results indicate that an alpha-level substantially higher than those normally used may be appropriate for risk properties under a wide range of loss functions. The paper also generalizes some known analytical results in the pretest literature as well as proving other results only previously shown numerically.

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