On Asymptotic Normality of Cross Data Matrix-Based PCA in High Dimension Low Sample Size
- 2019-11-28 (Thu.), 11:00 AM
- R6005, Research Center for Environmental Changes Building
- The reception will be held at 10:40 at the R6005, Research Center for Environmental Changes Building
- Dr. Shao-Hsuan Wang
- Institute of Statistical Science, Academia Sinica
Abstract
Principal component analysis in high dimension low sample size setting has been an active research area in recent years. Yata and Aoshima (2010) proposed a cross data matrix-based method and showed the asymptotic normality for estimates of spiked eigenvalues and also consistency for corresponding estimates of PC directions. However, the asymptotic normality for estimates of PC directions is still lacking. In this work, we have extended Yata and Aoshima (2010)'s study to include the investigation of the asymptotic normality for the leading CDM-based PC directions and to compare it with the asymptotic normality for the classical PCA. Numerical examples are provided to illustrate the asymptotic normality.
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