Parallel Statistical Computing for Statistical Inference

Abstract

Parallel statistical computing is an interesting and topical problem, driven by recent growth in the size of statistical data sets and the availability of network computing. This article reviews parallel statistical computing in regression analysis, nonparametric inference, and stochastic processes. In particular, we describe a range of methods including parallel multisplitting and the parallel QR method for least squares estimation in linear regression, parallel computing methods for nonlinear regression, the theoretical framework of the parallel bootstrap in nonparametric inference, preconditioner methods for Markov chains, and parallel Markov-chain Monte Carlo methods. We conclude that there is a need for further research in parallel statistical computing, and describe some of the important unsolved problems.

Keywords:

• 62G07
• 62G09
• 62J02
• 62J05
• 58J65

Keywords:

• Nonparametric inference
• Regression
• Statistical computing
• Stochastic processes

Acknowledgments

The author thanks the referees, the associate editor, and the joint editor for their remarks and suggestions, which have led to substantial improvements of the article. This work was supported by the NSFC under grant 10921101, 11171189.