Semiparametric Regression with Kernel Error Model
We propose and study a class of regression models, in which the mean function is specified parametricaUy as in the existing regression methods, but the residual distribution is modelled non-parametrically by a kernel estimator, without imposing any assumption on its distribution. This specification...
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| Veröffentlicht in: | Scandinavian journal of statistics 2007-12, Vol.34 (4), p.841-869 |
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| container_title | Scandinavian journal of statistics |
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| creator | YUAN, AO DE GOOIJER, JAN G. |
| description | We propose and study a class of regression models, in which the mean function is specified parametricaUy as in the existing regression methods, but the residual distribution is modelled non-parametrically by a kernel estimator, without imposing any assumption on its distribution. This specification is different from the existing semiparametric regression models. The asymptotic properties of such likelihood and the maximum likelihood estimate (MLE) under this semiparametric model are studied. We show that under some regularity conditions, the MLE under this model is consistent (when compared with the possibly pseudo-consistency of the parameter estimation under the existing parametric regression model), is asymptotically normal with rate $\sqrt n $ and efficient. The non-parametric pseudo-likelihood ratio has the Wilks property as the true likelihood ratio does. Simulated examples are presented to evaluate the accuracy of the proposed semiparametric MLE method. |
| doi_str_mv | 10.1111/j.1467-9469.2006.00531.x |
| format | Article |
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This specification is different from the existing semiparametric regression models. The asymptotic properties of such likelihood and the maximum likelihood estimate (MLE) under this semiparametric model are studied. We show that under some regularity conditions, the MLE under this model is consistent (when compared with the possibly pseudo-consistency of the parameter estimation under the existing parametric regression model), is asymptotically normal with rate $\sqrt n $ and efficient. The non-parametric pseudo-likelihood ratio has the Wilks property as the true likelihood ratio does. 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Simulated examples are presented to evaluate the accuracy of the proposed semiparametric MLE method.</description><subject>Density estimation</subject><subject>Distribution theory</subject><subject>Entropy</subject><subject>Errors</subject><subject>Estimation methods</subject><subject>Estimators</subject><subject>Exact sciences and technology</subject><subject>General topics</subject><subject>information bound</subject><subject>kernel density estimator</subject><subject>Linear inference, regression</subject><subject>Mathematics</subject><subject>maximum likelihood estimate</subject><subject>Maximum likelihood estimation</subject><subject>nonlinear regression</subject><subject>Parameter estimation</subject><subject>Parametric inference</subject><subject>Parametric models</subject><subject>Probability and statistics</subject><subject>Probability theory and stochastic processes</subject><subject>Random variables</subject><subject>Regression analysis</subject><subject>Sciences and techniques of general use</subject><subject>semiparametric model</subject><subject>Semiparametric modeling</subject><subject>Statistical variance</subject><subject>Statistics</subject><subject>U-statistic</subject><subject>Wilks property</subject><issn>0303-6898</issn><issn>1467-9469</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2007</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNqNkF-L1DAUxYMoOK5-BKEIPrYmTZo_Dz7Iso6uowvOiuDLJU1v3NbOtJt03Zlvb2qX8dXATULu-d0cDiEZowVL601XMCFVboQ0RUmpLCitOCsOj8jq1HhMVpRTnktt9FPyLMaOUiYF0yvCtrhrRxvsDqfQuuwr_gwYYzvss_t2usk-Ydhjn12EMITs89Bg_5w88baP-OLhPCPf3l9cn3_IN1frj-fvNrmrhGK5qlErV0rPvVW0rGvGKeraCeWt08xUSrmaK-ebEqXwjWs8lSWvFVLZGMv4GXm1zB3DcHuHcYJuuAv79CWUVDNV0qpMIr2IXBhiDOhhDO3OhiMwCnM-0MEcA8wxwJwP_M0HDgm9XNCAI7oTV_c2ui5OFn4Dt1yk7ZgqoSodbar5aUylBQOdpt5MuzTs9YPZRNveB7t3bfxnxhjGmTRJ93bR3bc9Hv_bLGwvr7bplviXC58cDuHEC1YJXWmR-vnSb-OEh1Pfhl8gFVcVfP-yBrOR9Idga7jmfwCec6ne</recordid><startdate>200712</startdate><enddate>200712</enddate><creator>YUAN, AO</creator><creator>DE GOOIJER, JAN G.</creator><general>Blackwell Publishing Ltd</general><general>Blackwell Publishing</general><general>Blackwell</general><general>Danish Society for Theoretical Statistics</general><scope>BSCLL</scope><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>H8D</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>200712</creationdate><title>Semiparametric Regression with Kernel Error Model</title><author>YUAN, AO ; DE GOOIJER, JAN G.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c5471-7be87c26f3fa702bb130e8bc47fac819577cb37cfd2e64fdcdf0623b7e06d9a13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2007</creationdate><topic>Density estimation</topic><topic>Distribution theory</topic><topic>Entropy</topic><topic>Errors</topic><topic>Estimation methods</topic><topic>Estimators</topic><topic>Exact sciences and technology</topic><topic>General topics</topic><topic>information bound</topic><topic>kernel density estimator</topic><topic>Linear inference, regression</topic><topic>Mathematics</topic><topic>maximum likelihood estimate</topic><topic>Maximum likelihood estimation</topic><topic>nonlinear regression</topic><topic>Parameter estimation</topic><topic>Parametric inference</topic><topic>Parametric models</topic><topic>Probability and statistics</topic><topic>Probability theory and stochastic processes</topic><topic>Random variables</topic><topic>Regression analysis</topic><topic>Sciences and techniques of general use</topic><topic>semiparametric model</topic><topic>Semiparametric modeling</topic><topic>Statistical variance</topic><topic>Statistics</topic><topic>U-statistic</topic><topic>Wilks property</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>YUAN, AO</creatorcontrib><creatorcontrib>DE GOOIJER, JAN G.</creatorcontrib><collection>Istex</collection><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>Scandinavian journal of statistics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>YUAN, AO</au><au>DE GOOIJER, JAN G.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Semiparametric Regression with Kernel Error Model</atitle><jtitle>Scandinavian journal of statistics</jtitle><date>2007-12</date><risdate>2007</risdate><volume>34</volume><issue>4</issue><spage>841</spage><epage>869</epage><pages>841-869</pages><issn>0303-6898</issn><eissn>1467-9469</eissn><abstract>We propose and study a class of regression models, in which the mean function is specified parametricaUy as in the existing regression methods, but the residual distribution is modelled non-parametrically by a kernel estimator, without imposing any assumption on its distribution. This specification is different from the existing semiparametric regression models. The asymptotic properties of such likelihood and the maximum likelihood estimate (MLE) under this semiparametric model are studied. We show that under some regularity conditions, the MLE under this model is consistent (when compared with the possibly pseudo-consistency of the parameter estimation under the existing parametric regression model), is asymptotically normal with rate $\sqrt n $ and efficient. The non-parametric pseudo-likelihood ratio has the Wilks property as the true likelihood ratio does. Simulated examples are presented to evaluate the accuracy of the proposed semiparametric MLE method.</abstract><cop>Oxford, UK</cop><pub>Blackwell Publishing Ltd</pub><doi>10.1111/j.1467-9469.2006.00531.x</doi><tpages>29</tpages><oa>free_for_read</oa></addata></record> |
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| ispartof | Scandinavian journal of statistics, 2007-12, Vol.34 (4), p.841-869 |
| issn | 0303-6898 1467-9469 |
| language | eng |
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| source | RePEc; Wiley Online Library Journals Frontfile Complete; JSTOR Mathematics & Statistics; EBSCOhost Business Source Complete; Jstor Complete Legacy |
| subjects | Density estimation Distribution theory Entropy Errors Estimation methods Estimators Exact sciences and technology General topics information bound kernel density estimator Linear inference, regression Mathematics maximum likelihood estimate Maximum likelihood estimation nonlinear regression Parameter estimation Parametric inference Parametric models Probability and statistics Probability theory and stochastic processes Random variables Regression analysis Sciences and techniques of general use semiparametric model Semiparametric modeling Statistical variance Statistics U-statistic Wilks property |
| title | Semiparametric Regression with Kernel Error Model |
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