Robust test procedures for multivariate data

The commonly used methods for analyzing multivariate data are based upon an assumption of multivariate normality. In this dissertation we develop some tests of this assumption and study their operating characteristics through a simulation study. An application of the proposed new test procedures shows that many illustrative data in principal monographs do not satisfy the assumption. We then proceed to develop robust analogues of Hotelling's {dollar}Tsp2{dollar} a classical and basic test in multivariate analysis.; Hotelling's {dollar}Tsp2{dollar}-test for significance of a mean vector is known to be variously optimal under the assumption of multivariate normality. However, its inappropriateness when the underlying assumption is incorrect is well established in several recent studies. Nonparametric alternatives to {dollar}Tsp2{dollar} are essentially asymptotic in nature and inconvenient to use. Moreover they are, in general, less efficient. Robust methods for multivariate problems are in rudimentary stages. We propose a trimmed means analogue {dollar}tilde Tsp2,{dollar} of the {dollar}Tsp2{dollar} statistic, and of Mudholkar and Subbaiah's (1980) asymptotic equivalents based upon the stepwise approach and Fisher, Logit, Loptak, and Tippett methods of combination.; The one sample robust alternatives are extended to the problem of testing equality of two mean vectors. The operating characteristics of the classical tests and the new robust alternatives are studied and compared using Monte Carlo experiments. It is demonstrated that the proposed test procedures are significantly superior when the underlying distributions are heavy tailed without costing too high a penalty when the assumption of multivariate normality is correct. Their use is illustrated by considering a variety of well known applications and data. In addition to the one and two sample problems these include testing symmetry in multivariate setting, and testing univariate linear model hypotheses encountered in experimental designs such as randomized block design.