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Abstract Details

Activity Number: 613
Type: Contributed
Date/Time: Thursday, August 2, 2012 : 8:30 AM to 10:20 AM
Sponsor: Section on Statistical Learning and Data Mining
Abstract - #305063
Title: A Bootstrap Estimator of the Rank of Random Matrices and Its Application
Author(s): Wei Luo*+ and Bing Li
Companies: Penn State University and Penn State University
Address: 425 Waupelani Drive Apt 418, State College, PA, 16801, United States
Keywords: Bootstrap ; Mallows metric ; candidate matrix ; eigenspace

Determining of the rank of a random matrix is critically important for many statistical inference problems such as dimension reduction and variable selection. Ye and Weiss (2003) proposed a bootstrap estimator, which has been widely used for dimension reduction because of its many advantages. However, in spite of its popularity and often superb numerical performance, its asymptotic behavior has never been carefully investigated. In this work we show that, under fairly realistic conditions, this estimator, if translated into the minimizer of an objective function, is in fact inconsistent, and we give a set of sufficient conditions under which it is consistent. Furthermore, we introduce a modification of this estimator to make the minimizer of the new objective function consistent in a very general setting. This modification makes use of both eigenvectors and eigenvalues, which in a sense combines the advantages of the bootstrap estimator and the BIC-type criteria. We compare this new estimator with several popular order-determination methods, and apply it to data analysis.

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