RARE-EVENT ANALYSIS FOR EXTREMAL EIGENVALUES OF WHITE WISHART MATRICES

• 成果类型: Article
• 署名作者: Jiang, Tiefeng; Leder, Kevin; Xu, Gongjun
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; University of Minnesota System; University of Minnesota Twin Cities; University of Michigan System; University of Michigan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/16-AOS1502
• 发表日期: 2017
• 页码: 1609-1637
• 关键词: monte-carlo; distributions

摘要

In this paper, we consider the extreme behavior of the extremal eigenvalues of white Wishart matrices, which plays an important role in multivariate analysis. In particular, we focus on the case when the dimension of the feature p is much larger than or comparable to the number of observations n, a common situation in modern data analysis. We provide asymptotic approximations and bounds for the tail probabilities of the extremal eigenvalues. Moreover, we construct efficient Monte Carlo simulation algorithms to compute the tail probabilities. Simulation results show that our method has the best performance among known approximation approaches, and furthermore provides an efficient and accurate way for evaluating the tail probabilities in practice.