Spatial aggregation of local likelihood estimates with applications to classification

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dc.creatorBelomestny, Denis
dc.creatorSpokoiny, Vladimir
dc.date2007-12-06
dc.date.accessioned2026-07-07T08:49:28Z
dc.date.available2026-07-07T08:49:28Z
dc.descriptionThis 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.
dc.descriptionPublished in at http://dx.doi.org/10.1214/009053607000000271 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)
dc.identifierhttps://arxiv.org/abs/0712.0939
dc.identifierhttp://arxiv.org/abs/0712.0939
dc.identifierAnnals of Statistics 2007, Vol. 35, No. 5, 2287-2311
dc.identifierdoi:10.1214/009053607000000271
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/144306
dc.subjectStatistics Theory
dc.subject62G05 (Primary); 62G07, 62G08, 62G32, 62H30 (Secondary)
dc.titleSpatial aggregation of local likelihood estimates with applications to classification
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