Spatial aggregation of local likelihood estimates with applications to classification

Denis Belomestny, Vladimir Spokoiny

Результат исследований: Вклад в журналСтатьярецензирование

17 Цитирования (Scopus)

Аннотация

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.

Язык оригиналаАнглийский
Страницы (с-по)2287-2311
Число страниц25
ЖурналAnnals of Statistics
Том35
Номер выпуска5
DOI
СостояниеОпубликовано - окт. 2007
Опубликовано для внешнего пользованияДа

Fingerprint

Подробные сведения о темах исследования «Spatial aggregation of local likelihood estimates with applications to classification». Вместе они формируют уникальный семантический отпечаток (fingerprint).

Цитировать