Estimation of cusp location of stochastic processes

a survey

S. Dachian, N. Kordzakhia, Yu A. Kutoyants*, A. Novikov

*Corresponding author for this work

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

We present a review of some recent results on estimation of location parameter for several models of observations with cusp-type singularity at the change point. We suppose that the cusp-type models fit better to the real phenomena described usually by change point models. The list of models includes Gaussian, inhomogeneous Poisson, ergodic diffusion processes, time series and the classical case of i.i.d. observations. We describe the properties of the maximum likelihood and Bayes estimators under some asymptotic assumptions. The asymptotic efficiency of estimators are discussed as well and the results of some numerical simulations are presented. We provide some heuristic arguments which demonstrate the convergence of log-likelihood ratios in the models under consideration to the fractional Brownian motion.

Original languageEnglish
Pages (from-to)345-362
Number of pages18
JournalStatistical Inference for Stochastic Processes
Volume21
Issue number2
DOIs
Publication statusPublished - 1 Jul 2018

Keywords

  • Change-point models
  • Cusp-type singularity
  • Diffusion processes
  • Fractional Brownian motion
  • Inhomogeneous Poisson processes
  • Maximum likelihood and Bayes estimators

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