NONPARAMETRIC ESTIMATION BY CONVEX PROGRAMMING

• 成果类型: Article
• 署名作者: Juditsky, Anatoli B.; Nemirovski, Arkadi S.
• 署名单位: University System of Georgia; Georgia Institute of Technology; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Inria
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/08-AOS654
• 发表日期: 2009
• 页码: 2278-2300
• 关键词: Adaptive Estimation; rates

摘要

The problem we concentrate on is as follows: given (1) a convex compact set X in R-n, an affine mapping x bar right arrow A(x), a parametric family {p(mu)(.)} of probability densities and (2) N i.i.d. observations of the random variable omega, distributed with the density p(A(x)) (.) for some (unknown) x is an element of X, estimate the value g(T)x of a given linear form at x. For several families {p(mu)(.)} with no additional assumptions on X and A, we develop computationally efficient estimation routines which are minimax optimal, within an absolute constant factor. We then apply these routines to recovering x itself in the Euclidean norm.