A confidence interval for the number of principal components
Chen, P.
2006 Journal of Statistical Planning and Inference, 136(8): 2630-2639
Keywords: Asymptotic distribution; Confidence limit; Covariance matrix; Eigenvalue; Principal component analysis
Chen, P., (2006), "A confidence interval for the number of principal components", Journal of Statistical Planning and Inference, 136(8): 2630-2639.
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 ? i is called important if ? i / ? 1 is sufficiently close to 1 where ? 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.
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