Monte Carlo Calibration of Distributions of Partition Statistics

In recursive partitioning (decision trees) a search is made for each factor as to how to best make a split. Because of this searching over many possibilities, the p-values for the split itself do not have the claimed distribution. Most often a p-value multiplicity correction is made using the Bonferroni adjustment. It turns out that this strongly overcorrects, and thus we investigated fitting the distribution to obtain better p-values.