Asymptotic properties of parallel Bayesian kernel density estimators

TL;DR

This paper analyzes the long-term behavior of parallel Bayesian kernel density estimators, focusing on their mean integrated squared error and optimal bandwidth choices when data is partitioned.

Contribution

It provides the first asymptotic expansion of the mean integrated squared error for these estimators and explores optimal bandwidth selection in a parallel setting.

Findings

Partitioning data affects bandwidth choice for optimal estimation.

Asymptotic expansion of mean integrated squared error derived.

Guidelines for bandwidth selection in parallel Bayesian kernel density estimation.

Abstract

In this article we perform an asymptotic analysis of Bayesian parallel kernel density estimators introduced by Neiswanger, Wang and Xing (2014). We derive the asymptotic expansion of the mean integrated squared error for the full data posterior estimator and investigate the properties of asymptotically optimal bandwidth parameters. Our analysis demonstrates that partitioning data into subsets requires a non-trivial choice of bandwidth parameters that optimizes the estimation error.