Penalized Weighted Variance Estimate for Dimension Reduction

Abstract

Sliced average variance estimate (SAVE) and sliced inverse regression are proven effective for dimension reduction. As an improvement of SAVE, weighted variance estimate (WVE) developed recently performs well in general situation. However, WVE, developed by slicing the range of Y, has difficulty in dealing with the case of Y being multivariate. The authors show that slicing can be viewed as a special penalty function. From this perspective, they develop a general method called Penalized Weighted Variance Estimate (PWVE), which provides a uniform procedure no matter the dimension of Y. Simulation results confirm the advantages of PWVE.

Keywords:

• Central space
• Dimension reduction
• Sliced average variance estimate
• Sliced inverse regression
• Weighted variance estimate

Mathematics Subject Classification:

• 62G08
• 62H05

Acknowledgment

The work of Dr. Zhao is supported by the National Natural Science Foundation of China (No. 11101022 and No. 11026049) and the Ministry of Education Humanities and Social Science Foundation Youth project (No. 10YJC910013) and the Fundamental Research Funds for the Central Universities. Prof. Xu is supported by the National Natural Science Foundation of China (No. 11071015). The authors are grateful for the associate editor and the referees for their valuable comments and suggestions, which greatly improved the presentation of this article.