Variable selection bias in regression trees with constant fits

The greedy search approach to variable selection in regression trees with constant fits is considered. At each node, the method usually compares the maximally selected statistic associated with each variable and selects the variable with the largest value to form the split. This method is shown to have selection bias, if predictor variables have different numbers of missing values and the bias can be corrected by comparing the corresponding P-values instead. Methods related to some change-point problems are used to compute the P-values and their performances are studied