# Stat Colloquium [In-Person]: Dr. Snigdhansu (Ansu) Chatterje

### UMBC

Location

Mathematics/Psychology : 401

Date & Time

February 9, 2024, 11:00 am – 12:00 pm

Description

**Title**: On
multivariate and infinite-dimensional quantiles and statistical depth functions

**Abstract**: For
absolutely continuous real random variables, the cumulative distribution
function is known to be a strictly increasing function, and the quantile
function is defined as its inverse. Minor adjustment to the definition allows
us to define quantile functions for other real random variables that may not
have strictly increasing cumulative distributions, while retaining all
desirable properties. How does one define quantiles in dimensions greater than
one? In this overview talk, we will discuss an alternative and equivalent definition
of a quantile, and how that definition can generalize to higher dimensions,
including many cases where the dimension may be infinite. We will look at some
interesting probabilistic and geometric properties of such multivariate
quantiles. In one dimension, sample quantiles also allow us to rank and order
the observations. A partial equivalent in higher dimensions is the notion of a
statistical depth function (or data-depth, as is often commonly called), and
our overview will also include discussions of properties and uses of the depth
function.

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