FORWARD AND BACKWARD ALGORITHMS FOR SELECTING PREDICTORS ON THE BASIS OF THE CRITERION FROM PREDICTION SUM OF SQUARES AND THEIR APPLICATION

In this paper, two fast algorithms for selecting predictors, the forward and backward algorithms, are proposed on the basis of the criterion from prediction sum of squares QPRESS). Not only would the numbers of the regression equation calculating PRESS value reduce from 2p-1 to at most p (p+1)/2, but also the amount of calculation for every PRESS value is much decreased, when either algorithm is used. The application in the long-range weather forecast shows that these algorithms have higher prediction skill as compared with stepwise regression.