CART Leaf Summaries via Bootstrap Bias Correction

CART provides interpretable tree models, but its data-adaptive construction can distort inference for terminal-node summaries. Comparing fitted trees with large independent reference samples, we find that regression terminal-node means are generally well calibrated, whereas standard deviations tend to be underestimated; in binary classification, terminal-node class proportions are often overly extreme, leading to downward-biased Bernoulli variance estimates. We propose a bootstrap bias correction (BBC) procedure that accounts for variation in tree structure by matching bootstrap-tree nodes to those of the original tree using observation overlap. Across simulations, BBC reduces error in regression standard deviations under nonlinear signal structures and improves class-probability and variance estimation in classification. Its benefits diminish, and it may slightly overcorrect, when the true tree structure is recovered nearly perfectly and uncorrected error is already small. Applications to Major League Baseball salary and Pima diabetes data illustrate BBC as a practical approach for mitigating adaptive distortion in CART terminal-node estimation.