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

Nino E. Kordzakhia; Yury A. Kutoyants; Alexander A. Novikov; Lin Yee Hin

doi:10.1016/j.spl.2018.04.004

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

Nino E. Kordzakhia^*, Yury A. Kutoyants, Alexander A. Novikov, Lin Yee Hin

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	141-151
Number of pages	11
Journal	Statistics and Probability Letters
Volume	139
DOIs	https://doi.org/10.1016/j.spl.2018.04.004
Publication status	Published - 1 Aug 2018

Keywords

Bayesian estimators
Fractional Brownian motion
Irregular statistical experiments
Location parameter
Maximum likelihood estimators

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10.1016/j.spl.2018.04.004

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

abstract = "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",

keywords = "Bayesian estimators, Fractional Brownian motion, Irregular statistical experiments, Location parameter, Maximum likelihood estimators",

author = "Kordzakhia, \{Nino E.\} and Kutoyants, \{Yury A.\} and Novikov, \{Alexander A.\} and Hin, \{Lin Yee\}",

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AU - Kordzakhia, Nino E.

AU - Kutoyants, Yury A.

AU - Novikov, Alexander A.

AU - Hin, Lin Yee

PY - 2018/8/1

Y1 - 2018/8/1

N2 - 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

AB - 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

KW - Bayesian estimators

KW - Fractional Brownian motion

KW - Irregular statistical experiments

KW - Location parameter

KW - Maximum likelihood estimators

UR - https://www.scopus.com/pages/publications/85046713917

U2 - 10.1016/j.spl.2018.04.004

DO - 10.1016/j.spl.2018.04.004

M3 - Article

AN - SCOPUS:85046713917

SN - 0167-7152

VL - 139

SP - 141

EP - 151

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

ER -

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

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Keywords

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