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October 2007 Spatial aggregation of local likelihood estimates with applications to classification
Denis Belomestny, Vladimir Spokoiny
Ann. Statist. 35(5): 2287-2311 (October 2007). DOI: 10.1214/009053607000000271

Abstract

This paper presents a new method for spatially adaptive local (constant) likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of the method is, given a sequence of local likelihood estimates (“weak” estimates), to construct a new aggregated estimate whose pointwise risk is of order of the smallest risk among all “weak” estimates. We also propose a new approach toward selecting the parameters of the procedure by providing the prescribed behavior of the resulting estimate in the simple parametric situation. We establish a number of important theoretical results concerning the optimality of the aggregated estimate. In particular, our “oracle” result claims that its risk is, up to some logarithmic multiplier, equal to the smallest risk for the given family of estimates. The performance of the procedure is illustrated by application to the classification problem. A numerical study demonstrates its reasonable performance in simulated and real-life examples.

Citation

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Denis Belomestny. Vladimir Spokoiny. "Spatial aggregation of local likelihood estimates with applications to classification." Ann. Statist. 35 (5) 2287 - 2311, October 2007. https://doi.org/10.1214/009053607000000271

Information

Published: October 2007
First available in Project Euclid: 7 November 2007

zbMATH: 1126.62021
MathSciNet: MR2363972
Digital Object Identifier: 10.1214/009053607000000271

Subjects:
Primary: 62G05
Secondary: 62G07, 62G08, 62G32, 62H30

Rights: Copyright © 2007 Institute of Mathematical Statistics

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Vol.35 • No. 5 • October 2007
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