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Estimating a class of diffusions from discrete observations via approximate maximum likelihood method
An approximate maximum likelihood method of estimation of diffusion parameters based on discrete observations of a diffusion X along fixed time-interval and Euler approximation of integrals is analysed. We assume that X satisfies a stochastic differential equation (SDE) of form , with non-random ini...
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| Published in: | Statistics (Berlin, DDR) DDR), 2018-03, Vol.52 (2), p.239-272 |
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| Language: | English |
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| container_title | Statistics (Berlin, DDR) |
| container_volume | 52 |
| creator | Huzak, Miljenko |
| description | An approximate maximum likelihood method of estimation of diffusion parameters
based on discrete observations of a diffusion X along fixed time-interval
and Euler approximation of integrals is analysed. We assume that X satisfies a stochastic differential equation (SDE) of form
, with non-random initial condition. SDE is nonlinear in
generally. Based on assumption that maximum likelihood estimator
of the drift parameter based on continuous observation of a path over
exists we prove that measurable estimator
of the parameters obtained from discrete observations of X along
by maximization of the approximate log-likelihood function exists,
being consistent and asymptotically normal, and
tends to zero with rate
in probability when
tends to zero with T fixed. The same holds in case of an ergodic diffusion when T goes to infinity in a way that
goes to zero with equidistant sampling, and we applied these to show consistency and asymptotical normality of
,
and asymptotic efficiency of
in this case. |
| doi_str_mv | 10.1080/02331888.2017.1382496 |
| format | article |
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based on discrete observations of a diffusion X along fixed time-interval
and Euler approximation of integrals is analysed. We assume that X satisfies a stochastic differential equation (SDE) of form
, with non-random initial condition. SDE is nonlinear in
generally. Based on assumption that maximum likelihood estimator
of the drift parameter based on continuous observation of a path over
exists we prove that measurable estimator
of the parameters obtained from discrete observations of X along
by maximization of the approximate log-likelihood function exists,
being consistent and asymptotically normal, and
tends to zero with rate
in probability when
tends to zero with T fixed. The same holds in case of an ergodic diffusion when T goes to infinity in a way that
goes to zero with equidistant sampling, and we applied these to show consistency and asymptotical normality of
,
and asymptotic efficiency of
in this case.</description><identifier>ISSN: 0233-1888</identifier><identifier>EISSN: 1029-4910</identifier><identifier>DOI: 10.1080/02331888.2017.1382496</identifier><language>eng</language><publisher>Abingdon: Taylor & Francis</publisher><subject>Asymptotic properties ; Differential equations ; Diffusion ; diffusion processes ; discrete observation ; Maximum likelihood estimation ; Maximum likelihood estimators ; Maximum likelihood method ; Normality ; Parameter estimation ; Parameters</subject><ispartof>Statistics (Berlin, DDR), 2018-03, Vol.52 (2), p.239-272</ispartof><rights>2017 Informa UK Limited, trading as Taylor & Francis Group 2017</rights><rights>2017 Informa UK Limited, trading as Taylor & Francis Group</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c338t-582c49958b2bc4f2a9ef28cb6f0101934d577ee7772c24aef18a65a89fa0cfdc3</citedby><cites>FETCH-LOGICAL-c338t-582c49958b2bc4f2a9ef28cb6f0101934d577ee7772c24aef18a65a89fa0cfdc3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>314,777,781,27905,27906</link.rule.ids></links><search><creatorcontrib>Huzak, Miljenko</creatorcontrib><title>Estimating a class of diffusions from discrete observations via approximate maximum likelihood method</title><title>Statistics (Berlin, DDR)</title><description>An approximate maximum likelihood method of estimation of diffusion parameters
based on discrete observations of a diffusion X along fixed time-interval
and Euler approximation of integrals is analysed. We assume that X satisfies a stochastic differential equation (SDE) of form
, with non-random initial condition. SDE is nonlinear in
generally. Based on assumption that maximum likelihood estimator
of the drift parameter based on continuous observation of a path over
exists we prove that measurable estimator
of the parameters obtained from discrete observations of X along
by maximization of the approximate log-likelihood function exists,
being consistent and asymptotically normal, and
tends to zero with rate
in probability when
tends to zero with T fixed. The same holds in case of an ergodic diffusion when T goes to infinity in a way that
goes to zero with equidistant sampling, and we applied these to show consistency and asymptotical normality of
,
and asymptotic efficiency of
in this case.</description><subject>Asymptotic properties</subject><subject>Differential equations</subject><subject>Diffusion</subject><subject>diffusion processes</subject><subject>discrete observation</subject><subject>Maximum likelihood estimation</subject><subject>Maximum likelihood estimators</subject><subject>Maximum likelihood method</subject><subject>Normality</subject><subject>Parameter estimation</subject><subject>Parameters</subject><issn>0233-1888</issn><issn>1029-4910</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2018</creationdate><recordtype>article</recordtype><recordid>eNp9kMtOwzAQRS0EEqXwCUiWWKf4kcT2DlSVh1SJDawtx7GpSxIX2yn073FU2LKaGfncO54LwDVGC4w4ukWEUsw5XxCE2QJTTkpRn4AZRkQUpcDoFMwmppigc3AR4xYhVFPKZsCsYnK9Sm54hwrqTsUIvYWts3aMzg8R2uD7PEcdTDLQN9GEfeanp71TUO12wX9PFgb2KjdjDzv3YTq38b6FvUkb316CM6u6aK5-6xy8Paxel0_F-uXxeXm_LjSlPBUVJ7oUouINaXRpiRLGEq6b2iKMsKBlWzFmDGOMaFIqYzFXdaW4sApp22o6BzdH3_ynz9HEJLd-DENeKXM2hLNSUJap6kjp4GMMxspdyAeEg8RITonKv0QnFZO_iWbd3VHnButDr7586FqZ1KHzwQY1aBcl_d_iB3FQfzM</recordid><startdate>20180304</startdate><enddate>20180304</enddate><creator>Huzak, Miljenko</creator><general>Taylor & Francis</general><general>Taylor & Francis Ltd</general><scope>AAYXX</scope><scope>CITATION</scope></search><sort><creationdate>20180304</creationdate><title>Estimating a class of diffusions from discrete observations via approximate maximum likelihood method</title><author>Huzak, Miljenko</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c338t-582c49958b2bc4f2a9ef28cb6f0101934d577ee7772c24aef18a65a89fa0cfdc3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2018</creationdate><topic>Asymptotic properties</topic><topic>Differential equations</topic><topic>Diffusion</topic><topic>diffusion processes</topic><topic>discrete observation</topic><topic>Maximum likelihood estimation</topic><topic>Maximum likelihood estimators</topic><topic>Maximum likelihood method</topic><topic>Normality</topic><topic>Parameter estimation</topic><topic>Parameters</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Huzak, Miljenko</creatorcontrib><collection>CrossRef</collection><jtitle>Statistics (Berlin, DDR)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Huzak, Miljenko</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Estimating a class of diffusions from discrete observations via approximate maximum likelihood method</atitle><jtitle>Statistics (Berlin, DDR)</jtitle><date>2018-03-04</date><risdate>2018</risdate><volume>52</volume><issue>2</issue><spage>239</spage><epage>272</epage><pages>239-272</pages><issn>0233-1888</issn><eissn>1029-4910</eissn><abstract>An approximate maximum likelihood method of estimation of diffusion parameters
based on discrete observations of a diffusion X along fixed time-interval
and Euler approximation of integrals is analysed. We assume that X satisfies a stochastic differential equation (SDE) of form
, with non-random initial condition. SDE is nonlinear in
generally. Based on assumption that maximum likelihood estimator
of the drift parameter based on continuous observation of a path over
exists we prove that measurable estimator
of the parameters obtained from discrete observations of X along
by maximization of the approximate log-likelihood function exists,
being consistent and asymptotically normal, and
tends to zero with rate
in probability when
tends to zero with T fixed. The same holds in case of an ergodic diffusion when T goes to infinity in a way that
goes to zero with equidistant sampling, and we applied these to show consistency and asymptotical normality of
,
and asymptotic efficiency of
in this case.</abstract><cop>Abingdon</cop><pub>Taylor & Francis</pub><doi>10.1080/02331888.2017.1382496</doi><tpages>34</tpages></addata></record> |
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| ispartof | Statistics (Berlin, DDR), 2018-03, Vol.52 (2), p.239-272 |
| issn | 0233-1888 1029-4910 |
| language | eng |
| recordid | cdi_proquest_journals_2012874937 |
| source | Taylor and Francis Science and Technology Collection |
| subjects | Asymptotic properties Differential equations Diffusion diffusion processes discrete observation Maximum likelihood estimation Maximum likelihood estimators Maximum likelihood method Normality Parameter estimation Parameters |
| title | Estimating a class of diffusions from discrete observations via approximate maximum likelihood method |
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