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 journalArticle

2 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 languageEnglish
Pages (from-to)141-151
Number of pages11
JournalStatistics and Probability Letters
Volume139
DOIs
Publication statusPublished - 1 Aug 2018

Keywords

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

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