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

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 (f...

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Bibliographic Details
Published inStatistics & probability letters Vol. 139; pp. 141 - 151
Main Authors Kordzakhia, Nino E., Kutoyants, Yury A., Novikov, Alexander A., Hin, Lin-Yee
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.08.2018
Subjects
Bayesian estimators
Fractional Brownian motion
Irregular statistical experiments
Location parameter
Maximum likelihood estimators
Maximum likelihood estimators
Location parameter
Bayesian estimators
Irregular statistical experiments
Fractional Brownian motion
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Summary: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.
ISSN:0167-7152
1879-2103
DOI:10.1016/j.spl.2018.04.004