Consistency of Estimation Criteria of Dimensionality in Principal Component Analysis

Day & Time
5th June 2015, 15:00~
Venue
RERF Hijiyama Hall
Lecturer
Prof. Yasunori Fujikoshi
(Emeritus Professor, Advisor of the SSRC, Hiroshima University)
Presentation Title
Consistency of Estimation Criteria of Dimensionality in Principal Component Analysis
Outline
Principal component analysis (PCA) is a method for the reduction of dimensionality of the data in the form of n observations of p variables. The population components and their variances are defined by using the characteristic roots and vectors of the covariance matrix of the p variables. We consider a covariance matrix structure with dimension j such that the first j largest characteristic roots are different and the remainder roots are the same. Such a model can be found in many data sets, and is also obtained from a spiked covariance model. In general, we need to estimate the dimensionality. Our purpose is to give consistency of estimation criteria based on model selection criteria under high-dimensional framework as well as large-sample framework. The theoretical results in the case of non-normality are obtained by using random matrix theory. Simulation results are also given. The present work is based on Fujikoshi and Sakurai (2015) and Bai, Fujikoshi and Choi (2015).