### 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 |

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### Keywords

- Asymptotic distribution
- Confidence limit
- Covariance matrix
- Eigenvalue
- Principal component analysis

### ASJC Scopus subject areas

- Statistics, Probability and Uncertainty
- Applied Mathematics
- Statistics and Probability

### Cite this

**A confidence interval for the number of principal components.** / Chen, Pinyuen.

Research output: Contribution to journal › Article

*Journal of Statistical Planning and Inference*, vol. 136, no. 8, pp. 2630-2639. https://doi.org/10.1016/j.jspi.2004.10.016

}

TY - JOUR

T1 - A confidence interval for the number of principal components

AU - Chen, Pinyuen

PY - 2006/8/1

Y1 - 2006/8/1

N2 - 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.

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

KW - Principal component analysis

UR - http://www.scopus.com/inward/record.url?scp=33645929409&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645929409&partnerID=8YFLogxK

U2 - 10.1016/j.jspi.2004.10.016

DO - 10.1016/j.jspi.2004.10.016

M3 - Article

AN - SCOPUS:33645929409

VL - 136

SP - 2630

EP - 2639

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 8

ER -