Variable Selection by C_p Statistic in Multiple Responses Regression with Fewer Sample Size Than the Dimension

摘要

In this paper, we introduce a better statistical method about model selection, and contribute to updating data mining technique. We consider the problem of selecting q explanatory variables out of k (q < k), when the dimension p of the response variables is larger than the sample size n in the multiple responses regression. We consider C_p statistic which is an estimator of the sum of standardized mean square errors. The standardization uses the inverse of the variance-covariance matrix of p response variables and thus the estimator of the inverse of the sample variance-covariance matrix. However, since n < p, such an inverse matrix cannot be used. Thus, we use the Moore-Penrose inverse and define the C_p statistic. Such a statistic0 will be denoted by C_p+ . An example is given to illustrate the use of C_p+ statistic. The performance is demonstrated by simulation result and real data study.