Generalized Regression Trees: Function Estimation via Recursive Partitioning andMaximum Likelihood

摘要

A method that blends tree-structured nonparametric regression with classicalmaximum likelihood is used in a generalized regression setting. The function estimates constructed are piecewise polynomials and are produced together with decision trees containing useful information on the regressors. Fitting is carried out by applying maximum likelihood estimation to subsets of the data, where the subsets are selected via recursive partitioning and cross-validation pruning. Examples of Poisson and logistic regression trees are given to illustrate the method applied to count and binary response data. Large-sample properties of the estimates are derived under appropriate regularity conditions. Generalized linear models, Anscombe residual, pseudo residual, Vapnik-Chervonenkis class, consistency.