Big Data Analysis via Multivariate Confidence Distribution

Abstract

A confidence distribution (CD) is loosely defined as a sample-dependent distribution function on the parameter space that can represent confidence sets of all levels for a parameter of interest. Recent developments of CD-based inferential tools mainly focus on inference of scalar parameters yet the multi-parameter regime is rarely touched. Moreover, the CD concept is convenient for synthesizing evidence from independent sources. In this talk, we will propose CD-based divide-and-conquer approaches for multivariate inference of Big Data. The methodological efficacy of the proposed approaches when the number of data partitions diverges with the total sample size is shown in theoretical results. Empirical evaluation of statistical and computational performance is carried out by a simulation study and a real data illustration.