One-Way MANOVA of High-Dimension with a Small Sample Size

• Activity Number: 533
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: International Chinese Statistical Association
• Author(s): Jiajuan Liang*
• Keywords: analysis of variance ; F-test ; high dimension ; multiple mean comparisons ; principal component

Abstract

One-way multivariate analysis of variance (MAVOVA) is a natural extension to the univariate one-way ANOVA when there are multiple dependent and independent variables within the model which the researcher wishes to test. When assuming no interaction effects, we can reduce the problem of MANOVA to the problem of testing the statistical hypothesis: H0: µ1=µ2=...=µk, versus H1: at least two means differ, where µi (a p×1 vector) stands for the mean main effect from group i ( i=1, 2, ., k for some finite number k). Let ni be the sample size from group i and n=n1+.+nk be the total sample size. It is well-known that in the case of high dimension p with a small sample size n (n?p), under the regular normal assumption, the classical Wilks Lambda-statistic for testing the above hypothesis is no longer applicable. In this paper we will develop a series of exact F-tests for the above hypothesis that are applicable for both cases of n>p and n?p by using the theory of spherical distributions and the idea of principal component analysis. The power of the proposed F-tests will be studied by Monte Carlo simulation. An application of the proposed F-tests will be illustrated by a real example.