Functional Cramer-Rao bounds and Stein estimators in Sobolev spaces, for Brownian motion and Cox processes

被引：1

作者：

Musta, Eni ^{[1
]}

Pratelli, Maurizio ^{[2
]}

Trevisan, Dario ^{[2
]}

机构：

[1] Delft Univ Technol, Delft, Netherlands

[2] Univ Pisa, Pisa, Italy

来源：

JOURNAL OF MULTIVARIATE ANALYSIS | 2017年 / 154卷

关键词：

Cramer-Rao bound; Stein phenomenon; Malliavin calculus; Cox model; MALLIAVIN CALCULUS;

D O I：

10.1016/j.jmva.2016.10.011

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：

We investigate the problems of drift estimation for a shifted Brownian motion and intensity estimation for a Cox process on a finite interval [0, T], when the risk is given by the energy functional associated to some fractional Sobolev space H-0(1) subset of W-alpha,W-2 subset of L-2. In both situations, Cramer-Rao lower bounds are obtained, entailing in particular that no unbiased estimators (not necessarily adapted) with finite risk in H-0(1) exist. By Malliavin calculus techniques, we also study super-efficient Stein type estimators (in the Gaussian case). (C) 2016 Elsevier Inc. All rights reserved.

引用

页码：135 / 146

页数：12

共 13 条

[1] STEIN ESTIMATION OF THE INTENSITY OF A SPATIAL HOMOGENEOUS POISSON POINT PROCESS [J].