MULTIVARIATE NORMAL APPROXIMATION WITH STEIN'S METHOD OF EXCHANGEABLE PAIRS UNDER A GENERAL LINEARITY CONDITION

• 成果类型: Article
• 署名作者: Reinert, Gesine; Roellin, Adrian
• 署名单位: University of Oxford; National University of Singapore
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/09-AOP467
• 发表日期: 2009
• 页码: 2150-2173
• 关键词: CENTRAL-LIMIT-THEOREM; clt; CONVERGENCE

摘要

In this paper we establish a multivariate exchangeable pairs approach within the framework of Stein's method to assess distributional distances to potentially singular multivariate normal distributions. By extending the statistics into a higher-dimensional space, we also propose an embedding method which allows for a normal approximation even when the corresponding statistics of interest do not lend themselves easily to Stein's exchangeable pairs approach. To illustrate the method, we provide the examples of runs on the line as well as double-indexed permutation statistics.