A ROBBINS-MONRO PROCEDURE FOR ESTIMATION IN SEMIPARAMETRIC REGRESSION MODELS
This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins-Monro procedure. On the one hand, we propose a stochastic algorithm similar...
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| Veröffentlicht in: | The Annals of statistics 2012-04, Vol.40 (2), p.666-693 |
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| container_title | The Annals of statistics |
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| creator | Bercu, Bernard Fraysse, Philippe |
| description | This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins-Monro procedure. On the one hand, we propose a stochastic algorithm similar to that of Robbins-Monro in order to estimate the shift parameter. A preliminary evaluation of the regression function is not necessary to estimate the shift parameter. On the other hand, we make use of a recursive Nadaraya-Watson estimator for the estimation of the regression function. This kernel estimator takes into account the previous estimation of the shift parameter. We establish the almost sure convergence for both Robbins-Monro and Nadaraya-Watson estimators. The asymptotic normality of our estimates is also provided. Finally, we illustrate our semiparametric estimation procedure on simulated and real data. |
| doi_str_mv | 10.1214/12-AOS969 |
| format | Article |
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We implement a very efficient and easy to handle Robbins-Monro procedure. On the one hand, we propose a stochastic algorithm similar to that of Robbins-Monro in order to estimate the shift parameter. A preliminary evaluation of the regression function is not necessary to estimate the shift parameter. On the other hand, we make use of a recursive Nadaraya-Watson estimator for the estimation of the regression function. This kernel estimator takes into account the previous estimation of the shift parameter. We establish the almost sure convergence for both Robbins-Monro and Nadaraya-Watson estimators. The asymptotic normality of our estimates is also provided. Finally, we illustrate our semiparametric estimation procedure on simulated and real data.</description><identifier>ISSN: 0090-5364</identifier><identifier>EISSN: 2168-8966</identifier><identifier>DOI: 10.1214/12-AOS969</identifier><language>eng</language><publisher>Hayward: Institute of Mathematical Statistics</publisher><subject>62G05 ; 62G20 ; asymptotic properties ; Confidence interval ; Density estimation ; Electrocardiography ; Estimating techniques ; estimation of a regression function ; estimation of a shift ; Estimators ; Martingales ; Mathematics ; Maximum likelihood estimation ; Parameter estimation ; Perceptron convergence procedure ; Probability ; Random variables ; Regression analysis ; Semiparametric estimation ; Shape functions ; Statistics ; Statistics Theory ; Studies</subject><ispartof>The Annals of statistics, 2012-04, Vol.40 (2), p.666-693</ispartof><rights>Copyright © 2011 Institute of Mathematical Statistics</rights><rights>Copyright Institute of Mathematical Statistics Apr 2012</rights><rights>Distributed under a Creative Commons Attribution 4.0 International License</rights><rights>Copyright 2012 Institute of Mathematical Statistics</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c405t-5e650265e84a65e1f4d868e8d4ced1aedcd12f2b38cb016edd45a71aaa046e563</citedby><cites>FETCH-LOGICAL-c405t-5e650265e84a65e1f4d868e8d4ced1aedcd12f2b38cb016edd45a71aaa046e563</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/41713651$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/41713651$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>230,314,780,784,803,832,885,926,27924,27925,58017,58021,58250,58254</link.rule.ids><backlink>$$Uhttps://hal.science/hal-00551832$$DView record in HAL$$Hfree_for_read</backlink></links><search><creatorcontrib>Bercu, Bernard</creatorcontrib><creatorcontrib>Fraysse, Philippe</creatorcontrib><title>A ROBBINS-MONRO PROCEDURE FOR ESTIMATION IN SEMIPARAMETRIC REGRESSION MODELS</title><title>The Annals of statistics</title><description>This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins-Monro procedure. On the one hand, we propose a stochastic algorithm similar to that of Robbins-Monro in order to estimate the shift parameter. A preliminary evaluation of the regression function is not necessary to estimate the shift parameter. On the other hand, we make use of a recursive Nadaraya-Watson estimator for the estimation of the regression function. This kernel estimator takes into account the previous estimation of the shift parameter. We establish the almost sure convergence for both Robbins-Monro and Nadaraya-Watson estimators. The asymptotic normality of our estimates is also provided. Finally, we illustrate our semiparametric estimation procedure on simulated and real data.</description><subject>62G05</subject><subject>62G20</subject><subject>asymptotic properties</subject><subject>Confidence interval</subject><subject>Density estimation</subject><subject>Electrocardiography</subject><subject>Estimating techniques</subject><subject>estimation of a regression function</subject><subject>estimation of a shift</subject><subject>Estimators</subject><subject>Martingales</subject><subject>Mathematics</subject><subject>Maximum likelihood estimation</subject><subject>Parameter estimation</subject><subject>Perceptron convergence procedure</subject><subject>Probability</subject><subject>Random variables</subject><subject>Regression analysis</subject><subject>Semiparametric estimation</subject><subject>Shape functions</subject><subject>Statistics</subject><subject>Statistics Theory</subject><subject>Studies</subject><issn>0090-5364</issn><issn>2168-8966</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2012</creationdate><recordtype>article</recordtype><recordid>eNpVkU1Lw0AQhhdRsFYP_gAh4MlDdGe_urkZ060GkmzZtOdlTbbYUo0mreC_N6Wl4mUGZt55hpkXoWvA90CAPQAJY11GIjpBAwJChjIS4hQNMI5wyKlg5-ii61YYYx4xOkBZHBj99JQWZZjrwuhganSixnOjgok2gSpnaR7PUl0EaRGUKk-nsYlzNTNpEhj1bFRZ7pq5HqusvERnC7fu_NUhD9F8ombJS5jp5zSJs7BimG9C7gXHRHAvmesjLFgthfSyZpWvwfm6qoEsyCuV1SsG4euacTcC5xxmwnNBh-hxz_1sm5WvNn5brZe1_WyX7679sY1b2mSeHaqH5JrOAqUjIiTBskfc7RFvbv1v8CXO7K7WP4iDpOQbeu3tcd3X1ncbu2q27Ud_oQVMRcQphtEfsWqbrmv94ogFbHfe9MHuvem1N3vtqts07VHIYARUcKC_FS2DJA</recordid><startdate>20120401</startdate><enddate>20120401</enddate><creator>Bercu, Bernard</creator><creator>Fraysse, Philippe</creator><general>Institute of Mathematical Statistics</general><general>The Institute of Mathematical Statistics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope><scope>1XC</scope><scope>VOOES</scope></search><sort><creationdate>20120401</creationdate><title>A ROBBINS-MONRO PROCEDURE FOR ESTIMATION IN SEMIPARAMETRIC REGRESSION MODELS</title><author>Bercu, Bernard ; Fraysse, Philippe</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c405t-5e650265e84a65e1f4d868e8d4ced1aedcd12f2b38cb016edd45a71aaa046e563</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2012</creationdate><topic>62G05</topic><topic>62G20</topic><topic>asymptotic properties</topic><topic>Confidence interval</topic><topic>Density estimation</topic><topic>Electrocardiography</topic><topic>Estimating techniques</topic><topic>estimation of a regression function</topic><topic>estimation of a shift</topic><topic>Estimators</topic><topic>Martingales</topic><topic>Mathematics</topic><topic>Maximum likelihood estimation</topic><topic>Parameter estimation</topic><topic>Perceptron convergence procedure</topic><topic>Probability</topic><topic>Random variables</topic><topic>Regression analysis</topic><topic>Semiparametric estimation</topic><topic>Shape functions</topic><topic>Statistics</topic><topic>Statistics Theory</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Bercu, Bernard</creatorcontrib><creatorcontrib>Fraysse, Philippe</creatorcontrib><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><collection>Hyper Article en Ligne (HAL)</collection><collection>Hyper Article en Ligne (HAL) (Open Access)</collection><jtitle>The Annals of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Bercu, Bernard</au><au>Fraysse, Philippe</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>A ROBBINS-MONRO PROCEDURE FOR ESTIMATION IN SEMIPARAMETRIC REGRESSION MODELS</atitle><jtitle>The Annals of statistics</jtitle><date>2012-04-01</date><risdate>2012</risdate><volume>40</volume><issue>2</issue><spage>666</spage><epage>693</epage><pages>666-693</pages><issn>0090-5364</issn><eissn>2168-8966</eissn><abstract>This paper is devoted to the parametric estimation of a shift together with the nonparametric estimation of a regression function in a semiparametric regression model. We implement a very efficient and easy to handle Robbins-Monro procedure. On the one hand, we propose a stochastic algorithm similar to that of Robbins-Monro in order to estimate the shift parameter. A preliminary evaluation of the regression function is not necessary to estimate the shift parameter. On the other hand, we make use of a recursive Nadaraya-Watson estimator for the estimation of the regression function. This kernel estimator takes into account the previous estimation of the shift parameter. We establish the almost sure convergence for both Robbins-Monro and Nadaraya-Watson estimators. The asymptotic normality of our estimates is also provided. Finally, we illustrate our semiparametric estimation procedure on simulated and real data.</abstract><cop>Hayward</cop><pub>Institute of Mathematical Statistics</pub><doi>10.1214/12-AOS969</doi><tpages>28</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | The Annals of statistics, 2012-04, Vol.40 (2), p.666-693 |
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| language | eng |
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| source | JSTOR Mathematics and Statistics; EZB-FREE-00999 freely available EZB journals; Project Euclid Complete; JSTOR |
| subjects | 62G05 62G20 asymptotic properties Confidence interval Density estimation Electrocardiography Estimating techniques estimation of a regression function estimation of a shift Estimators Martingales Mathematics Maximum likelihood estimation Parameter estimation Perceptron convergence procedure Probability Random variables Regression analysis Semiparametric estimation Shape functions Statistics Statistics Theory Studies |
| title | A ROBBINS-MONRO PROCEDURE FOR ESTIMATION IN SEMIPARAMETRIC REGRESSION MODELS |
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