JSM 2004 - Toronto

Abstract #300370

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Activity Number: 404
Type: Contributed
Date/Time: Thursday, August 12, 2004 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Computing
Abstract - #300370
Title: Inference on General Linear Regression Models with Unequal Error Variances
Author(s): Shun-Yi Chen*+ and Miin-jye Wen
Companies: Tamkang University and National Cheng Kung University
Address: Dept. of Mathematics, Tamsui, International, 251, Taiwan
Keywords: one-sample procedure ; heteroscedasticity ; t distribution ; hypothesis testing
Abstract:

A one-sample procedure is proposed for statistical inference on a general linear regression model with unknown and possibly unequal normal error variances. The goal is (1) to test the null hypothesis that the response variable is free of all on-hand predictor variables, and (2) to test the null hypothesis that a subset of predictor variables are unimportant. Two new test statistics based on weighted sample means at each predictor's data points are proposed. It turns out that these test statistics have sampling distributions completely independent of the unknown variances, and the p values of these test statistics can be calculated by simulation. The item (1) can used to test the treatment effects for one-way layout ANOVA model and the test (2) can be applied to regression model selection problem when one predictor variable is considered at a time as well to test the row and column effects, respectively, in a two-way layout ANOVA model.

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