THE VARIABLE SELECTION PROBLEM FOR PREDICTION ON THE PREDICTION AREA DIFFERENT FROM SAMPLE AREA

Abstract

In the regression model Y_α=x_α'β+ε_α (α=1, 2, …, n), we discuss the variable selection problem for prediction of the future dependent variable Y^* on the future sample point x^*, where x^* is assumed to be a vector of random variables having a known probability density function. As the risk function for variable selection, the expectation with respect to x^* of Prediction Mean Square Error is used. Two criteria for variable selection are proposed and discussed on the basis of numerical examples.