Paul H Chook Department of Information Systems and Statistics,
Zicklin School of Business, Baruch College,
The City University of New York
摘要： In many statistical dimension reduction problems, including principal component analysis, canonical correlation analysis, independent component analysis, and sufficient dimension reduction, etc., it is often of interest to determine the rank of a matrix parameter based on a consistent matrix estimator. In this paper, we propose a method called the augmentation estimator for this purpose, with the aid of an augmentation predictor that is artificially generated and merged with the original predictor. Similar to Luo and Li (2016), the augmentation estimator uses information from both the eigenvalues and the eigenvectors of the matrix estimator. Compared with the existing order-determination methods, it is easy to implement, computationally efficient, consistent under general conditions, and applicable in high-dimensional cases. Its effectiveness is supported by simulation studies. The way we employ the augmentation predictor is novel, which may inspire independent research interest.
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