Equivalence theory for density estimation, Poisson processes and Gaussian white noise with drift

被引：39

作者：

Brown, LD ^{[1
]}

Carter, AV

Low, MG

Zhang, CH

机构：

[1] Univ Penn, Dept Stat, Wharton Sch, Philadelphia, PA 19104 USA

[2] Rutgers State Univ, Dept Stat, Piscataway, NJ 08854 USA

[3] Univ Calif Santa Barbara, Dept Stat & Appl Probabil, Santa Barbara, CA 93106 USA

来源：

ANNALS OF STATISTICS | 2004年 / 32卷 / 05期

关键词：

asymptotic equivalence; decision theory; local limit theorem; quantile transform; white noise model;

D O I：

10.1214/00905360400000012

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 establishes the global asymptotic equivalence between a Poisson process with variable intensity and white noise with drift under sharp smoothness conditions on the unknown function. This equivalence is also extended to density estimation models by Poissonization. The asymptotic equivalences are established by constructing explicit equivalence mappings. The impact of such asymptotic equivalence results is that an investigation in one of these nonparametric models automatically yields asymptotically analogous results in the other models.

引用

页码：2074 / 2097

页数：24