A confidence interval for the number of principal components

Pinyuen Chen

doi:10.1016/j.jspi.2004.10.016

A confidence interval for the number of principal components

Pinyuen Chen

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

This paper proposes a confidence interval for the number of important principal components in principal component analysis. An important principal component is defined as a principal component whose value is close to the value of the largest principal component. More specifically, a principal component λ_i is called important if λ_i / λ₁ is sufficiently close to 1 where λ₁ is the largest eigenvalue. A distance measure for closeness will be defined under the framework of ranking and selection theory. A confidence interval for the number of important principal components will be proposed using a stepwise selection procedure. The proposed interval, which is asymptotic in nature, includes the true important components with a specified confidence. Numerical examples are given to illustrate our procedure.

Original language	English (US)
Pages (from-to)	2630-2639
Number of pages	10
Journal	Journal of Statistical Planning and Inference
Volume	136
Issue number	8
DOIs	https://doi.org/10.1016/j.jspi.2004.10.016
State	Published - Aug 1 2006

Keywords

Asymptotic distribution
Confidence limit
Covariance matrix
Eigenvalue
Principal component analysis

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1016/j.jspi.2004.10.016

Cite this

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AB - This paper proposes a confidence interval for the number of important principal components in principal component analysis. An important principal component is defined as a principal component whose value is close to the value of the largest principal component. More specifically, a principal component λi is called important if λi / λ1 is sufficiently close to 1 where λ1 is the largest eigenvalue. A distance measure for closeness will be defined under the framework of ranking and selection theory. A confidence interval for the number of important principal components will be proposed using a stepwise selection procedure. The proposed interval, which is asymptotic in nature, includes the true important components with a specified confidence. Numerical examples are given to illustrate our procedure.

KW - Asymptotic distribution

KW - Confidence limit

KW - Covariance matrix

KW - Eigenvalue

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A confidence interval for the number of principal components

Abstract

Keywords

ASJC Scopus subject areas

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