Inference for General MANOVA Based on ANOVA-Type Statistic

Abstract

Inference methods for general multivariate analysis of variance (MANOVA) are studied. Homoscedasticity and any particular distribution are not assumed in general factorial designs under consideration. In that general framework, the existing methods based on the Wald-type statistic may behave poorly under finite samples, e.g., they are often too liberal under unbalanced designs and skewed distributions. In this paper, the testing procedures and confidence regions based on the ANOVA-type statistic and its standardized version are proposed, which usually perform very satisfactorily in cases where the known tests fail. Different approaches to approximate the null distribution of test statistics are developed. They are based on asymptotic distribution and bootstrap and permutation methods. The consistency of the asymptotic tests under fixed alternatives is proved. In simulation studies, it is shown that some of the new procedures possess good size and power characteristics, and they are competitive to existing procedures.