Convergence rate for predictive recursion estimation of finite mixtures

Details Convergence rate for predictive recursion estimation of finite mixtures Convergence rate for predictive recursion estimation of finite mixtures

2011-06-21

arxiv.org/abs/1106.4223v2

Statistics and Probability Letters, 82 (2012), pp. 378-384

Mathematics

Statistics Theory

12 pages, 1 figure

Scientific paper

10.1016/j.spl.2011.10.023

Predictive recursion (PR) is a fast stochastic algorithm for nonparametric estimation of mixing distributions in mixture models. It is known that the PR estimates of both the mixing and mixture densities are consistent under fairly mild conditions, but currently very little is known about the rate of convergence. Here I first investigate asymptotic convergence properties of the PR estimate under model misspecification in the special case of finite mixtures with known support. Tools from stochastic approximation theory are used to prove that the PR estimates converge, to the best Kullback--Leibler approximation, at a nearly root-$n$ rate. When the support is unknown, PR can be used to construct an objective function which, when optimized, yields an estimate the support. I apply the known-support results to derive a rate of convergence for this modified PR estimate in the unknown support case, which compares favorably to known optimal rates.

Affiliated with

Also associated with

No associations

Rating

Convergence rate for predictive recursion estimation of finite mixtures does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Convergence rate for predictive recursion estimation of finite mixtures, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Convergence rate for predictive recursion estimation of finite mixtures will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-178915