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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.
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