Semi-parametric estimation of partially linear single-index models
One of the most difficult problems in applications of semi-parametric partially linear single-index models (PLSIM) is the choice of pilot estimators and complexity parameters which may result in radically different estimators. Pilot estimators are often assumed to be root- n consistent, although the...
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| Veröffentlicht in: | Journal of multivariate analysis 2006-05, Vol.97 (5), p.1162-1184 |
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| container_title | Journal of multivariate analysis |
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| creator | Xia, Yingcun Härdle, Wolfgang |
| description | One of the most difficult problems in applications of semi-parametric partially linear single-index models (PLSIM) is the choice of pilot estimators and complexity parameters which may result in radically different estimators. Pilot estimators are often assumed to be root-
n
consistent, although they are not given in a constructible way. Complexity parameters, such as a smoothing bandwidth are constrained to a certain speed, which is rarely determinable in practical situations.
In this paper, efficient, constructible and practicable estimators of PLSIMs are designed with applications to time series. The proposed technique answers two questions from Carroll et al. [Generalized partially linear single-index models, J. Amer. Statist. Assoc. 92 (1997) 477–489]: no root-
n
pilot estimator for the single-index part of the model is needed and complexity parameters can be selected at the optimal smoothing rate. The asymptotic distribution is derived and the corresponding algorithm is easily implemented. Examples from real data sets (credit-scoring and environmental statistics) illustrate the technique and the proposed methodology of minimum average variance estimation (MAVE). |
| doi_str_mv | 10.1016/j.jmva.2005.11.005 |
| format | Article |
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n
consistent, although they are not given in a constructible way. Complexity parameters, such as a smoothing bandwidth are constrained to a certain speed, which is rarely determinable in practical situations.
In this paper, efficient, constructible and practicable estimators of PLSIMs are designed with applications to time series. The proposed technique answers two questions from Carroll et al. [Generalized partially linear single-index models, J. Amer. Statist. Assoc. 92 (1997) 477–489]: no root-
n
pilot estimator for the single-index part of the model is needed and complexity parameters can be selected at the optimal smoothing rate. The asymptotic distribution is derived and the corresponding algorithm is easily implemented. Examples from real data sets (credit-scoring and environmental statistics) illustrate the technique and the proposed methodology of minimum average variance estimation (MAVE).</description><identifier>ISSN: 0047-259X</identifier><identifier>EISSN: 1095-7243</identifier><identifier>DOI: 10.1016/j.jmva.2005.11.005</identifier><identifier>CODEN: JMVAAI</identifier><language>eng</language><publisher>San Diego, CA: Elsevier Inc</publisher><subject>Asymptotic distribution ; Asymptotic distribution Generalized partially linear model Local linear smoother Optimal consistency rate Single-index model ; Data analysis ; Estimating techniques ; Exact sciences and technology ; Generalized partially linear model ; Local linear smoother ; Mathematical models ; Mathematics ; Nonparametric inference ; Optimal consistency rate ; Parametric inference ; Probability and statistics ; Sciences and techniques of general use ; Single-index model ; Statistics ; Studies</subject><ispartof>Journal of multivariate analysis, 2006-05, Vol.97 (5), p.1162-1184</ispartof><rights>2005 Elsevier Inc.</rights><rights>2006 INIST-CNRS</rights><rights>Copyright Taylor & Francis Group May 2006</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c470t-359770732d45a59891ff737a26bbcf80d3544dd7fc8d1b5d2af1f0178d35161d3</citedby><cites>FETCH-LOGICAL-c470t-359770732d45a59891ff737a26bbcf80d3544dd7fc8d1b5d2af1f0178d35161d3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://dx.doi.org/10.1016/j.jmva.2005.11.005$$EHTML$$P50$$Gelsevier$$Hfree_for_read</linktohtml><link.rule.ids>314,778,782,3539,3996,27907,27908,45978</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=17693934$$DView record in Pascal Francis$$Hfree_for_read</backlink><backlink>$$Uhttp://econpapers.repec.org/article/eeejmvana/v_3a97_3ay_3a2006_3ai_3a5_3ap_3a1162-1184.htm$$DView record in RePEc$$Hfree_for_read</backlink></links><search><creatorcontrib>Xia, Yingcun</creatorcontrib><creatorcontrib>Härdle, Wolfgang</creatorcontrib><title>Semi-parametric estimation of partially linear single-index models</title><title>Journal of multivariate analysis</title><description>One of the most difficult problems in applications of semi-parametric partially linear single-index models (PLSIM) is the choice of pilot estimators and complexity parameters which may result in radically different estimators. Pilot estimators are often assumed to be root-
n
consistent, although they are not given in a constructible way. Complexity parameters, such as a smoothing bandwidth are constrained to a certain speed, which is rarely determinable in practical situations.
In this paper, efficient, constructible and practicable estimators of PLSIMs are designed with applications to time series. The proposed technique answers two questions from Carroll et al. [Generalized partially linear single-index models, J. Amer. Statist. Assoc. 92 (1997) 477–489]: no root-
n
pilot estimator for the single-index part of the model is needed and complexity parameters can be selected at the optimal smoothing rate. The asymptotic distribution is derived and the corresponding algorithm is easily implemented. Examples from real data sets (credit-scoring and environmental statistics) illustrate the technique and the proposed methodology of minimum average variance estimation (MAVE).</description><subject>Asymptotic distribution</subject><subject>Asymptotic distribution Generalized partially linear model Local linear smoother Optimal consistency rate Single-index model</subject><subject>Data analysis</subject><subject>Estimating techniques</subject><subject>Exact sciences and technology</subject><subject>Generalized partially linear model</subject><subject>Local linear smoother</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Nonparametric inference</subject><subject>Optimal consistency rate</subject><subject>Parametric inference</subject><subject>Probability and statistics</subject><subject>Sciences and techniques of general use</subject><subject>Single-index model</subject><subject>Statistics</subject><subject>Studies</subject><issn>0047-259X</issn><issn>1095-7243</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2006</creationdate><recordtype>article</recordtype><sourceid>X2L</sourceid><recordid>eNp9UE2LFDEUDOKC465_wFMjeOw2Lx-dbvCii18w4EEX9hYyyYum6S-T3sH5975hFr0ZqNThVb1UirGXwBvg0L4ZmmE6ukZwrhuAhugJ2wHvdW2Ekk_ZjnNlaqH7-2fseSkD5wDaqB17_w2nVK8uuwm3nHyFZUuT29IyV0usaLAlN46nakwzulyVNP8YsU5zwN_VtAQcyw27im4s-OKRr9ndxw_fbz_X-6-fvty-29deGb7VUvfGcCNFUNrpvushRiONE-3h4GPHg9RKhWCi7wIcdBAuQuRgOhpAC0Fes1eXvWtefj1QTjssD3mmJ62ArqWjJInEReTzUkrGaNdM_8knC9yeq7KDPVdlz1VZAEtEpv3FlHFF_9eBiGfp7OzRStcbuk4EcrZEiaAJKwGgFbSsU_bnNtG6149BXfFujNnNPpV_QUzby14q0r296KhEPCbMtviEs8eQMvrNhiX9L_UfWqGYLw</recordid><startdate>20060501</startdate><enddate>20060501</enddate><creator>Xia, Yingcun</creator><creator>Härdle, Wolfgang</creator><general>Elsevier Inc</general><general>Elsevier</general><general>Taylor & Francis LLC</general><scope>6I.</scope><scope>AAFTH</scope><scope>IQODW</scope><scope>DKI</scope><scope>X2L</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>JQ2</scope></search><sort><creationdate>20060501</creationdate><title>Semi-parametric estimation of partially linear single-index models</title><author>Xia, Yingcun ; Härdle, Wolfgang</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c470t-359770732d45a59891ff737a26bbcf80d3544dd7fc8d1b5d2af1f0178d35161d3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2006</creationdate><topic>Asymptotic distribution</topic><topic>Asymptotic distribution Generalized partially linear model Local linear smoother Optimal consistency rate Single-index model</topic><topic>Data analysis</topic><topic>Estimating techniques</topic><topic>Exact sciences and technology</topic><topic>Generalized partially linear model</topic><topic>Local linear smoother</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Nonparametric inference</topic><topic>Optimal consistency rate</topic><topic>Parametric inference</topic><topic>Probability and statistics</topic><topic>Sciences and techniques of general use</topic><topic>Single-index model</topic><topic>Statistics</topic><topic>Studies</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Xia, Yingcun</creatorcontrib><creatorcontrib>Härdle, Wolfgang</creatorcontrib><collection>ScienceDirect Open Access Titles</collection><collection>Elsevier:ScienceDirect:Open Access</collection><collection>Pascal-Francis</collection><collection>RePEc IDEAS</collection><collection>RePEc</collection><collection>CrossRef</collection><collection>ProQuest Computer Science Collection</collection><jtitle>Journal of multivariate analysis</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Xia, Yingcun</au><au>Härdle, Wolfgang</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Semi-parametric estimation of partially linear single-index models</atitle><jtitle>Journal of multivariate analysis</jtitle><date>2006-05-01</date><risdate>2006</risdate><volume>97</volume><issue>5</issue><spage>1162</spage><epage>1184</epage><pages>1162-1184</pages><issn>0047-259X</issn><eissn>1095-7243</eissn><coden>JMVAAI</coden><abstract>One of the most difficult problems in applications of semi-parametric partially linear single-index models (PLSIM) is the choice of pilot estimators and complexity parameters which may result in radically different estimators. Pilot estimators are often assumed to be root-
n
consistent, although they are not given in a constructible way. Complexity parameters, such as a smoothing bandwidth are constrained to a certain speed, which is rarely determinable in practical situations.
In this paper, efficient, constructible and practicable estimators of PLSIMs are designed with applications to time series. The proposed technique answers two questions from Carroll et al. [Generalized partially linear single-index models, J. Amer. Statist. Assoc. 92 (1997) 477–489]: no root-
n
pilot estimator for the single-index part of the model is needed and complexity parameters can be selected at the optimal smoothing rate. The asymptotic distribution is derived and the corresponding algorithm is easily implemented. Examples from real data sets (credit-scoring and environmental statistics) illustrate the technique and the proposed methodology of minimum average variance estimation (MAVE).</abstract><cop>San Diego, CA</cop><pub>Elsevier Inc</pub><doi>10.1016/j.jmva.2005.11.005</doi><tpages>23</tpages><oa>free_for_read</oa></addata></record> |
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| subjects | Asymptotic distribution Asymptotic distribution Generalized partially linear model Local linear smoother Optimal consistency rate Single-index model Data analysis Estimating techniques Exact sciences and technology Generalized partially linear model Local linear smoother Mathematical models Mathematics Nonparametric inference Optimal consistency rate Parametric inference Probability and statistics Sciences and techniques of general use Single-index model Statistics Studies |
| title | Semi-parametric estimation of partially linear single-index models |
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