Estimating linear functionals in Poisson mixture models

被引：2

作者：

Cavalier, Laurent ^{[1
]}

Hengartner, NicolasW. ^{[2
]}

机构：

[1] Univ Aix Marseille 1, CMI, Lab Anal Topol & Probabil, F-13453 Marseille 13, France

[2] Los Alamos Natl Lab, Dept Stat, Los Alamos, NM 87545 USA

来源：

JOURNAL OF NONPARAMETRIC STATISTICS | 2009年 / 21卷 / 06期

关键词：

Poisson mixtures; linear functionals; inverse problems; EXPONENTIAL FAMILY MODELS; MIXING DENSITIES; INVERSE PROBLEMS; DECONVOLUTION; RATES;

D O I：

10.1080/10485250902971716

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

This paper concerns the problem of estimating linear functionals of the mixing distribution from Poisson mixture observations. In particular, linear functionals for which a parametric rate of convergence cannot be achieved are studied. It appears that Gaussian functionals are rather easy to estimate. Estimation of the distribution functions is then considered by approximating this functional using Gaussian functionals. Finally, the case of smooth distribution functions is considered in order to deal with rather general linear functionals.

引用

页码：713 / 728

页数：16

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