Estimation of cusp location of stochastic processes: a survey

S. Dachian, N. Kordzakhia, Yu. A. Kutoyants () and A. Novikov
Additional contact information
S. Dachian: University of Lille
N. Kordzakhia: Macquarie University
Yu. A. Kutoyants: Le Mans University
A. Novikov: University of Technology Sydney

Statistical Inference for Stochastic Processes, 2018, vol. 21, issue 2, No 6, 345-362

Abstract: 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.

Keywords: Change-point models; Cusp-type singularity; Inhomogeneous Poisson processes; Diffusion processes; Maximum likelihood and Bayes estimators; Fractional Brownian motion (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11203-018-9171-2

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