Open Access
August 2017 Rare-event analysis for extremal eigenvalues of white Wishart matrices
Tiefeng Jiang, Kevin Leder, Gongjun Xu
Ann. Statist. 45(4): 1609-1637 (August 2017). DOI: 10.1214/16-AOS1502


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.


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Tiefeng Jiang. Kevin Leder. Gongjun Xu. "Rare-event analysis for extremal eigenvalues of white Wishart matrices." Ann. Statist. 45 (4) 1609 - 1637, August 2017.


Received: 1 April 2015; Revised: 1 July 2016; Published: August 2017
First available in Project Euclid: 28 June 2017

zbMATH: 1377.65013
MathSciNet: MR3670190
Digital Object Identifier: 10.1214/16-AOS1502

Primary: 60B20 , 65C05

Keywords: $\beta$-Laguerre ensemble , Extremal eigenvalues , importance sampling , Random matrix

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.45 • No. 4 • August 2017
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