Estimation of cusp location of stochastic processes: a survey

Dachian, S; Kordzakhia, N; Kutoyants, YA; Novikov, A

Estimation of cusp location of stochastic processes: a survey

Dachian, S Kordzakhia, N Kutoyants, YA Novikov, A

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Publication Type:: Journal Article
Citation:: Statistical Inference for Stochastic Processes, 2018, 21 (2), pp. 345 - 362
Issue Date:: 2018-07-01

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Field	Value	Language
dc.contributor.author	Dachian, S	en_US
dc.contributor.author	Kordzakhia, N	en_US
dc.contributor.author	Kutoyants, YA	en_US
dc.contributor.author	Novikov, A https://orcid.org/0000-0001-8529-173X	en_US
dc.date.issued	2018-07-01	en_US
dc.identifier.citation	Statistical Inference for Stochastic Processes, 2018, 21 (2), pp. 345 - 362	en_US
dc.identifier.issn	1387-0874	en_US
dc.identifier.uri	http://hdl.handle.net/10453/124804
dc.description.abstract	© 2018, Springer Science+Business Media B.V., part of Springer Nature. 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.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP150102758
dc.relation.ispartof	Statistical Inference for Stochastic Processes	en_US
dc.relation.isbasedon	10.1007/s11203-018-9171-2	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	Estimation of cusp location of stochastic processes: a survey	en_US
dc.type	Journal Article
utslib.citation.volume	2	en_US
utslib.citation.volume	21	en_US
utslib.for	0104 Statistics	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
pubs.organisational-group	/University of Technology Sydney/Strength - QFRC - Quantitative Finance Research Centre
utslib.copyright.status	open_access
pubs.issue	2	en_US
pubs.publication-status	Published	en_US
pubs.volume	21	en_US

Abstract:

© 2018, Springer Science+Business Media B.V., part of Springer Nature. 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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http://hdl.handle.net/10453/124804