Statistical Inference Based on Multivariate Ranks

Biman Chakraborty
Abstract
In the last two decades, there has been extensive work on extending the notions of quantiles and ranks for the multivariate data. In this talk, we will discuss some of these approaches, and various descriptive statistics based on them. Some of the natural questions that arise in the context of multivariate data are: Should multivariate analysis be carried out componentwise, or with full dimensionality, or pairwise? What are the notions of symmetry for the multivariate data? We will explore the concepts of rank functions in the contexts of these questions. We will also present some extensions of quantile-quantile plots and scale-scale plots based on ranks/quantiles as visualization tools for multivariate data.