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Generalized regression trees. (English) Zbl 0824.62060
Summary: 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.

MSC:
62J12 Generalized linear models (logistic models)
62G07 Density estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis
62J99 Linear inference, regression
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