Shyamal D. Peddada, PhD, Professor & Chair, Department of Biostatistics, will present, "Nonparametric procedures for testing order among multivariate distributions."
Comparison of two or more ordered experimental groups on the basis of multivariate data is a common problem of interest in a wide range of applications such as in economics, finance, toxicology, clinical trials, etc. Marginally, not only are the data not normally distributed, the shape of the distribution may even change with population (or experimental groups). Thus the data are not likely to be multivariate normally distributed. Secondly, from an application point of view, often researchers are not only interested in determining whether the experimental groups are different from each other but whether they are “ordered” (in some sense) in the response vector. Since the shape of the distribution may change over the experimental groups, it may not be sufficient or even meaningful to compare the mean vectors. For example, even though the population means are identical the probability distributions could be very different. Consequently, standard multivariate methods such as the multivariate analysis of variance (MANOVA) may not suitable. In this talk we describe some notions of stochastic ordering of multivariate random vectors and develop methodologies for testing such orders. Resulting methodologies are illustrated using some examples from toxicology. Time permitting, we shall discuss multivariate tests for the case of nearly singular distributions that can occur due to high dimensionality.