On cusp location estimation for perturbed dynamical systems

Kutoyants, Yury A.

doi:10.1111/sjos.12391

Cited by 4 publications

(2 citation statements)

References 21 publications

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“…In conclusion, let us note that some other models of observations were equally studied in presence of a cusptype singularity at the change-point by dierent authors. For nonlinear regression models we refer to Prakasa Rao [73], Döring [31], as well as to Döring and Jensen [32]; for delay dierential equations with noise we refer to Gushchin and Küchler [40]; and for dynamical systems with small noise we refer to Kutoyants [61]. These authors still obtain the same (fBm based) asymptotic behavior of the MLE and of the BEs.…”

Section: On Parameter Estimation In Non-regular Situations Of Cusp Typementioning

confidence: 93%

Change-point detection, segmentation, and related topics

Bardet¹,

Brault²,

Dachian³

et al. 2020

ESAIM: ProcS

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Recent contributions to change-point detection, segmentation and inference for non-regular models are presented. Various problems are considered including the multiple change-point estimation with adaptive penalty for time series with different dependency structures, estimation of the singularity point in cusp-type models, inference for thresholded autoregressive models, and cross-segmentation of matrices.

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Section: On Parameter Estimation In Non-regular Situations Of Cusp Typementioning

confidence: 93%

Change-point detection, segmentation, and related topics

Bardet¹,

Brault²,

Dachian³

et al. 2020

ESAIM: ProcS

View full text Add to dashboard Cite

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“…θε − ϑ 0 =⇒ ξ, convergence of moments of these estimators and the asymptotic efficiency of the BE. For the full proofs see [15].…”

Section: Ergodic Diffusion Processmentioning

confidence: 99%

Estimation of cusp location of stochastic processes: a survey

Dachian

Kordzakhia

Kutoyants

et al. 2018

Stat Inference Stoch Process

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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.

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