Heteroscedastic, Unbalanced, Two-Fold, Nested Model When the Number of Subclasses Is Large

• Activity Number: 141
• Type: Contributed
• Date/Time: Monday, August 4, 2008 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Shu-Min Liao*+ and Michael G. Akritas
• Companies: The Pennsylvania State University and The Pennsylvania State University
• Keywords: Nonparametric ; Nested models ; Heteroscedastic ; Unbalanced design ; Subclass effects ; Asymptotic theory

Abstract

At 2007 JSM, we have showed that in the homoscedastic balanced two-fold nested model, the classical normality-based F-test procedure for the sub-class effect is asymptotically valid. This year, we are going to present our latest findings about the two-fold nested model under heteroscedasticity and unbalanced design. The testing of the subclass effects when the number of sub-classes goes to infinity is still the core of our talk. We will show, via theoretical derivation and numerical evidence, that the classical F-test procedure is very sensitive to departures from homoscedasticity in both of balanced and unbalanced cases. As a consequence, two new test statistics (unweighted and weighted) are proposed for the heteroscedastic unbalanced cases, and their asymptotic distributions, both under the null and alternative hypotheses, are then established.