### 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} / λ_{1} is sufficiently close to 1 where λ_{1} 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) |
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Pages (from-to) | 2630-2639 |

Number of pages | 10 |

Journal | Journal of Statistical Planning and Inference |

Volume | 136 |

Issue number | 8 |

DOIs | |

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