Departmental Colloquium
Ryan Martin
IUPUI
Recursive nonparametric estimation of mixing distributions
Abstract: Mixture distributions make for useful statistical models, but
estimation of the mixing distribution itself is computationally and
theoretically challenging. Recent progress has been made with a fast,
online algorithm called predictive recursion (PR), which is capable of
producing a continuous estimate of the mixing density. While the
computational strengths of PR are readily apparent, good theoretical
properties have been much slower to develop. I will present a new and
general theorem which says that, if the mixture model is mis-specified,
then the PR estimate of the mixture density converges almost surely to
the Kullback-Leibler projection of the true density onto the model,
provided that the kernel satisfies a certain uniform
square-integrability condition. From this, almost sure weak convergence
of the PR estimate of the mixing distribution follows as a corollary.
The fact that PR is a special case of the Robbins-Monro stochastic
approximation process will be used to sketch a proof of the main
theorem. I will also give a bound on the rate of convergence, and
discuss its minimax nature. Some extensions, applications, and open
questions will also be considered.
Friday February 19, 2010 at 3:00 PM in SEO 636