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 journalArticlepeer-review

    5 Citations (Scopus)


    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
    Issue number2
    Publication statusPublished - 1 Jul 2018


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


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