Distribution-Free Tests for Unbalanced Heteroscedastic Longitudinal Data in High-Dimensional ANOVA Setting

• Activity Number: 98
• Type: Invited
• Date/Time: Monday, July 30, 2012 : 8:30 AM to 10:20 AM
• Sponsor: Journal of Nonparmametric Statistics
• Author(s): Haiyan Wang*+ and Ke Zhang and Raymond Carroll and Suojin Wang
• Companies: Kansas State University and University of North Dakota and Texas A&M University and Texas A&M University
• Keywords: Repeated measures ; Nonparametric Inference ; Hypothesis testing ; High dimensional multivariate analysis

Abstract

Here we consider a series of distribution free heteroscedastic tests for longitudinal data from unbalanced high dimensional ANOVA settings. We focus our attention on non-classical settings in which one or more factors have a large number of levels while the number of subjects is potentially limited. Different from the classical settings, our parameters of interest lie in a high dimensional space when at least one of the factors have a large number of levels. Heteroscedasticity and unbalancedness add additional limitation to classical test statistics commonly used in MANOVA or linear mixed effect models. Here, we propose new test statistics to adjust for both heteroscedasticity and unbalancedness. The hypotheses addressed here include both the effects of factors and their interactions that are commonly considered in MANOVA setting and the effects of time and the interaction between time and other factors that could be considered in linear mixed effect models but not in MANOVA. We then give the asymptotic distributions of our test statistics under current non-classical asymptotic setting. Numerical results including simulation study and a real data analysis will be presented.