On limit distributions of estimators in irregular statistical models and a new representation of fractional Brownian motion

被引：3

作者：

Kordzakhia, Nino E. ^{[1
]}

Kutoyants, Yury A. ^{[2
,3
,4
]}

Novikov, Alexander A. ^{[5
,6
]}

Hin, Lin-Yee ^{[5
]}

机构：

[1] Macquarie Univ, Sydney, NSW 2109, Australia

[2] Le Mans Univ, Le Mans, France

[3] Natl Res Univ MPEI, Moscow, Russia

[4] Tomsk State Univ, Int Lab Stat Stochast Proc & Quantitat Finance, Tomsk, Russia

[5] Univ Technol Sydney, Sydney, NSW 2007, Australia

[6] Steklov Inst Math, Moscow, Russia

来源：

STATISTICS & PROBABILITY LETTERS | 2018年 / 139卷

基金：

澳大利亚研究理事会; 俄罗斯科学基金会;

关键词：

Bayesian estimators; Maximum likelihood estimators; Location parameter; Irregular statistical experiments; Fractional Brownian motion; CUSP ESTIMATION; PITMAN ESTIMATORS; LOCATION; MAXIMUM;

D O I：

10.1016/j.spl.2018.04.004

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 provide new results concerning the limit distributions of Bayesian estimators (BE) and maximum likelihood estimators (MLE) of location parameters of cusp-type signals in "signal plus white noise" models. The limit distributions of BE and MLE are expressed in terms of fractional Brownian motion (fBm) with the Hurst parameter H, 0 < H < 1 as the noise intensity tends to zero. A new representation of fBm is given in terms of cusp functions. Simulation results for the densities and variances of the limit distributions of BE and MLE are also discussed. (C) 2018 Elsevier B.V. All rights reserved.

引用

页码：141 / 151

页数：11

共 30 条

[1]

[Anonymous], 2003, BAYESIAN NONPARAMETR

[2]

[Anonymous], 1998, Mathematical statistics

[3] On parameter estimation for cusp-type signals [J].