2007/10/01 by Denis Belomestny, Vladimir Spokoiny · 36 citations
Economics, Econometrics and Finance · Mathematics · #Applied mathematics #Econometrics #Economic and Environmental Valuation #Estimator #Gaussian #Mathematical optimization #Mathematics #Nonparametric statistics #Parametric model #Parametric statistics #Pointwise #Poisson distribution #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistics #math.ST #msc:62G05 #msc:62G07 #msc:62G08 #msc:62G32 #msc:62H30 #stat.TH
paper · pdf · doi:10.1214/009053607000000271
published in The Annals of Statistics 35(5) (Institute of Mathematical Statistics) · Published 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)
openalex publication_date 2007/10/01 · arxiv created 2007/12/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.