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Statistica Sinica 5(1995), 641-666


Probal Chaudhuri, Wen-Da Lo, Wei-Yin Loh and Ching-Ching Yang

Indian Statistical Institute, Chung Cheng Institute of Technology,
University of Wisconsin-Madison and Feng Chia University

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.

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