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Activity Number: 698
Type: Contributed
Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract #317576
Title: Selecting the Number of Principal Components: Estimation of the True Rank of a Noisy Matrix
Author(s): Yunjin Choi* and Rob Tibshirani and Jonathan Taylor
Companies: Stanford University and Stanford University and Stanford University
Keywords: Principal Component Analysis ; Hypothesis Testing ; Sequential Test

Principal component analysis (PCA) is a well-known tool in multivariate statistics. One big challenge in using the method is the choice of the number of components. In this paper, we propose an exact distribution-based method for this purpose: our approach is related to the adaptive regression framework of Taylor et al. (2013). Assuming Gaussian noise, we use the conditional distribution of the eigenvalues of a Wishart matrix as our test statistic, and derive exact hypothesis tests and confidence intervals for the true singular values. In simulation studies we find that our proposed method compares well to the proposal of Kritchman & Nadler (2008), which uses the asymptotic distribution of singular values based on the Tracy-Widom laws.

Authors who are presenting talks have a * after their name.

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