On Testing a General Linear Hypothesis Under Heteroscedasticity and Its Application

• Activity Number: 308
• Type: Contributed
• Date/Time: Tuesday, August 3, 2010 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Computing
• Author(s): Hubert Janpeing Chen*+
• Companies: National Cheng Kung University
• Keywords: Regression parameters ; One-stage Procedure ; Point estimation ; General linear hypothesis ; Confidence region ; Blood sugar level

Abstract

Assuming a general linear model with unknown and possibly unequal normal error variances, this paper is to develop a one-stage sampling procedure to handle the statistical inference problems involving point estimation, general linear hypothesis, and confidence region. The one-stage procedure is used to define a special weighted sample mean of responses at each point of predictors for constructing a general test statistic to test a general linear hypothesis. It is found that the distribution of the test statistic based on the one-stage sampling procedure under the hypothesis is exact and is completely independent of the unknown regression parameters and the unknown variances. Finally, the procedure with simulation program is applied to a real world data analysis problem in order to construct an appropriate prediction equation for fasting plasma glucose of humans on their ages and genders.