Kernelized goodness-of- fit tests for discrete variables

In this talk, we review goodness-of-fit tests for discrete distributions and propose an alternative
family of tests based on a kernelized Stein discrepancy. This measure is an expectation
based on Stein’s operator associated to the target distribution. It has some useful theoretical
and asymptotic properties and, furthermore, it can be empirically estimated. A key ingredient
for this procedure is the choice of an adequate kernel which may be related to the target
distribution.
In order to illustrate the efficiency of these tests, we resort to empirical analysis by simulations
based on the Binomial case and “close” distributions with respect to the total variation
distance.