# A confidence interval for the number of principal components

Research output: Contribution to journalArticle

2 Citations (Scopus)

### 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 language English (US) 2630-2639 10 Journal of Statistical Planning and Inference 136 8 https://doi.org/10.1016/j.jspi.2004.10.016 Published - Aug 1 2006

### Fingerprint

Principal Components
Principal component analysis
Confidence interval
Ranking and Selection
Largest Eigenvalue
Selection Procedures
Distance Measure
Principal Component Analysis
Confidence
Principal components
Numerical Examples
Interval

### 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

In: Journal of Statistical Planning and Inference, Vol. 136, No. 8, 01.08.2006, p. 2630-2639.

Research output: Contribution to journalArticle

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