A High-dimensionality-adjusted Consistent Cp-type Statistic for Selecting Variables in a Normality-assumed Linear Regression with Multiple Responses

In this paper, we consider the consistency of Cp-type statistics for selecting variables in a normality-assumed linear regression with multiple responses when the dimension of the vector of the response variables may be large. We propose a new consistent Cp-type statistic for which consistency can be achieved whenever the dimension of the response variables vector is fixed or goes to infinity. A high probability of selecting the true subset of explanatory variables can be expected under a moderate sample size when the proposed Cp-type statistic is used to select variables, even when there is a high-dimensional response variables vector