The principal correlation components estimator and its optimality

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• 作者：Wenxing Guo ; Xiaohui Liu ; Shangli Zhang
• 关键词：Principal correlation components estimator ; Least squares estimator ; Principal components regression estimator ; Admissible estimator ; Balanced loss function ; Pitman closeness criterion
• 刊名：Statistical Papers
• 出版年：2016
• 出版时间：September 2016
• 年：2016
• 卷：57
• 期：3
• 页码：755-779
• 全文大小：758 KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Statistics
  Statistics for Business, Economics, Mathematical Finance and Insurance
  Probability Theory and Stochastic Processes
  Economic Theory
  Operation Research and Decision Theory
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1613-9798
• 卷排序：57

文摘

In regression analysis, the principal components regression estimator (PCRE) is often used to alleviate the effect of multicollinearity by deleting the principal components variables with smaller eigenvalues, but it has some drawbacks for subset selection. So another effective estimator based on the principal components, termed the principal correlation components estimator (PCCE), has been proposed, which selects the variables by considering the correlation coefficients between the principal components variables and the response variable. In this paper we investigate the property of the PCCE and its optimality. We prove that the PCCE is an admissible estimator and obtain the condition that the PCCE performs better than the PCRE under the balanced loss function (BLF). As an improvement of the least squares estimator (LSE), the conditions that the PCCE performs better than LSE under the BLF and the Pitman closeness criterion are derived in the paper. The empirical performance of the PCCE is demonstrated by several real and simulation data examples.