Recursive estimation in hidden Markov models
We consider a hidden Markov model (HMM) with multidimensional observations, and where the coefficients (transition probability matrix, and observation conditional densities) depend on some unknown parameter. We study the asymptotic behaviour of two recursive estimators, the recursive maximum likelih...
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| creator | LeGland, F. Mevel, L. |
| description | We consider a hidden Markov model (HMM) with multidimensional observations, and where the coefficients (transition probability matrix, and observation conditional densities) depend on some unknown parameter. We study the asymptotic behaviour of two recursive estimators, the recursive maximum likelihood estimator (RMLE), and the recursive conditional least squares estimator (RCLSE), as the number of observations increases to infinity. Firstly, we exhibit the contrast functions associated with the two non-recursive estimators, and we prove that the recursive estimators converge a.s. to the set of stationary points of the corresponding contrast function. Secondly, we prove that the two recursive estimators are asymptotically normal. |
| doi_str_mv | 10.1109/CDC.1997.652384 |
| format | Conference Proceeding |
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We study the asymptotic behaviour of two recursive estimators, the recursive maximum likelihood estimator (RMLE), and the recursive conditional least squares estimator (RCLSE), as the number of observations increases to infinity. Firstly, we exhibit the contrast functions associated with the two non-recursive estimators, and we prove that the recursive estimators converge a.s. to the set of stationary points of the corresponding contrast function. Secondly, we prove that the two recursive estimators are asymptotically normal.</description><identifier>ISSN: 0191-2216</identifier><identifier>ISBN: 0780341872</identifier><identifier>ISBN: 9780780341876</identifier><identifier>DOI: 10.1109/CDC.1997.652384</identifier><language>eng</language><publisher>IEEE</publisher><subject>Convergence ; Covariance matrix ; Electronic mail ; Filters ; H infinity control ; Hidden Markov models ; Least squares approximation ; Maximum likelihood estimation ; Probability distribution ; Recursive estimation</subject><ispartof>Proceedings of the 36th IEEE Conference on Decision and Control, 1997, Vol.4, p.3468-3473 vol.4</ispartof><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c264t-43c472a586ccbb1a14e09e35b931f9f40cc36b5002f07f199e4a4f81fb2190213</citedby></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/652384$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>309,310,776,780,785,786,2051,4035,4036,27904,54898</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/652384$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc></links><search><creatorcontrib>LeGland, F.</creatorcontrib><creatorcontrib>Mevel, L.</creatorcontrib><title>Recursive estimation in hidden Markov models</title><title>Proceedings of the 36th IEEE Conference on Decision and Control</title><addtitle>CDC</addtitle><description>We consider a hidden Markov model (HMM) with multidimensional observations, and where the coefficients (transition probability matrix, and observation conditional densities) depend on some unknown parameter. We study the asymptotic behaviour of two recursive estimators, the recursive maximum likelihood estimator (RMLE), and the recursive conditional least squares estimator (RCLSE), as the number of observations increases to infinity. Firstly, we exhibit the contrast functions associated with the two non-recursive estimators, and we prove that the recursive estimators converge a.s. to the set of stationary points of the corresponding contrast function. Secondly, we prove that the two recursive estimators are asymptotically normal.</description><subject>Convergence</subject><subject>Covariance matrix</subject><subject>Electronic mail</subject><subject>Filters</subject><subject>H infinity control</subject><subject>Hidden Markov models</subject><subject>Least squares approximation</subject><subject>Maximum likelihood estimation</subject><subject>Probability distribution</subject><subject>Recursive estimation</subject><issn>0191-2216</issn><isbn>0780341872</isbn><isbn>9780780341876</isbn><fulltext>true</fulltext><rsrctype>conference_proceeding</rsrctype><creationdate>1997</creationdate><recordtype>conference_proceeding</recordtype><sourceid>6IE</sourceid><sourceid>RIE</sourceid><recordid>eNotj8tKAzEUQAMq2FbXgqt8gDPem2TyWMr4hJaC6LokmRuMtjMyGQv-vYW6OrvDOYxdIdSI4G7b-7ZG50ytGyGtOmFzMBakQmvEKZsBOqyEQH3O5qV8AoAFrWfs5pXiz1jynjiVKe_8lIee555_5K6jnq_8-DXs-W7oaFsu2Fny20KX_1yw98eHt_a5Wq6fXtq7ZRWFVlOlZFRG-MbqGENAj4rAkWyCk5hcUhCj1KEBEAlMOkST8ipZTEGgA4Fywa6P3kxEm-_xkDX-bo5j8g_8F0BK</recordid><startdate>1997</startdate><enddate>1997</enddate><creator>LeGland, F.</creator><creator>Mevel, L.</creator><general>IEEE</general><scope>6IE</scope><scope>6IL</scope><scope>CBEJK</scope><scope>RIE</scope><scope>RIL</scope></search><sort><creationdate>1997</creationdate><title>Recursive estimation in hidden Markov models</title><author>LeGland, F. ; Mevel, L.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c264t-43c472a586ccbb1a14e09e35b931f9f40cc36b5002f07f199e4a4f81fb2190213</frbrgroupid><rsrctype>conference_proceedings</rsrctype><prefilter>conference_proceedings</prefilter><language>eng</language><creationdate>1997</creationdate><topic>Convergence</topic><topic>Covariance matrix</topic><topic>Electronic mail</topic><topic>Filters</topic><topic>H infinity control</topic><topic>Hidden Markov models</topic><topic>Least squares approximation</topic><topic>Maximum likelihood estimation</topic><topic>Probability distribution</topic><topic>Recursive estimation</topic><toplevel>online_resources</toplevel><creatorcontrib>LeGland, F.</creatorcontrib><creatorcontrib>Mevel, L.</creatorcontrib><collection>IEEE Electronic Library (IEL) Conference Proceedings</collection><collection>IEEE Proceedings Order Plan All Online (POP All Online) 1998-present by volume</collection><collection>IEEE Xplore All Conference Proceedings</collection><collection>IEEE Electronic Library (IEL)</collection><collection>IEEE Proceedings Order Plans (POP All) 1998-Present</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>LeGland, F.</au><au>Mevel, L.</au><format>book</format><genre>proceeding</genre><ristype>CONF</ristype><atitle>Recursive estimation in hidden Markov models</atitle><btitle>Proceedings of the 36th IEEE Conference on Decision and Control</btitle><stitle>CDC</stitle><date>1997</date><risdate>1997</risdate><volume>4</volume><spage>3468</spage><epage>3473 vol.4</epage><pages>3468-3473 vol.4</pages><issn>0191-2216</issn><isbn>0780341872</isbn><isbn>9780780341876</isbn><abstract>We consider a hidden Markov model (HMM) with multidimensional observations, and where the coefficients (transition probability matrix, and observation conditional densities) depend on some unknown parameter. We study the asymptotic behaviour of two recursive estimators, the recursive maximum likelihood estimator (RMLE), and the recursive conditional least squares estimator (RCLSE), as the number of observations increases to infinity. Firstly, we exhibit the contrast functions associated with the two non-recursive estimators, and we prove that the recursive estimators converge a.s. to the set of stationary points of the corresponding contrast function. Secondly, we prove that the two recursive estimators are asymptotically normal.</abstract><pub>IEEE</pub><doi>10.1109/CDC.1997.652384</doi></addata></record> |
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| language | eng |
| recordid | cdi_ieee_primary_652384 |
| source | IEEE Electronic Library (IEL) Conference Proceedings |
| subjects | Convergence Covariance matrix Electronic mail Filters H infinity control Hidden Markov models Least squares approximation Maximum likelihood estimation Probability distribution Recursive estimation |
| title | Recursive estimation in hidden Markov models |
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