JSM 2004 - Toronto

Abstract #300363

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Activity Number: 116
Type: Contributed
Date/Time: Monday, August 9, 2004 : 10:30 AM to 12:20 PM
Sponsor: General Methodology
Abstract - #300363
Title: One-sample Regression Procedure for Testing a General Linear Hypothesis under Heterogeneous Error Variances
Author(s): Hubert J. Chen*+ and Miin-jye Wen
Companies: National Cheng Kung University and National Cheng Kung University
Address: 1 University Rd., Tainan, , Taiwan, ROC
Keywords: linear models ; heterocedasticity ; hypothesis testing ; confidence region ; Student's t distribution
Abstract:

Assuming a general linear model with unknown and possibly unequal normal error variances, the goal is to propose a one-sample testing procedure for testing a general linear hypothesis and constructing a confidence region concerning a set of estimable functions of regression parameters. A new test statistic is constructed based on a weighted sample mean at each of predictor's data points; it turns out to be a quadratic function of several independent Student's t random variables under the null hypothesis. As a result, the distribution of the proposed test statistic is completely independent of the unknown error variances. Hence, the p value and/or the critical values of such test can be obtained from computer simulation using SAS language for small samples, or approximated by a chi-squared distribution for large samples.

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