Abstract: A method of generalized regression that blends tree-structured nonparametric regression and adaptive recursive partitioning with maximum likelihood estimation is studied. The function estimate is a piecewise polynomial, with the pieces determined by the terminal nodes of a binary decision tree. The decision tree is constructed by recursively partitioning the data according to the signs of the residuals from a model fitted by maximum likelihood to each node. Algorithms for tree-structured Poisson and logistic regression and examples to illustrate them are given. Large-sample properties of the estimates are derived under appropriate regularity conditions.
Key words and phrases: Anscombe residual, consistency, generalized linear model, maximum likelihood, pseudo residual, recursive partitioning, Vapnik-Chervonenkis class.