A confidence interval for the number of principal components

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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 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.

Original languageEnglish (US)
Pages (from-to)2630-2639
Number of pages10
JournalJournal of Statistical Planning and Inference
Volume136
Issue number8
DOIs
StatePublished - 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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