Generalized Partially Linear Single-Index Models
The typical generalized linear model for a regression of a response Y on predictors (X, Z) has conditional mean function based on a linear combination of (X, Z). We generalize these models to have a nonparametric component, replacing the linear combination α T 0 X + β T 0 Z by η 0 (α T 0 X) + β T 0...
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| Veröffentlicht in: | Journal of the American Statistical Association 1997-06, Vol.92 (438), p.477-489 |
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| container_issue | 438 |
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| container_title | Journal of the American Statistical Association |
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| creator | Carroll, R. J. Fan, Jianqing Gijbels, Irène Wand, M. P. |
| description | The typical generalized linear model for a regression of a response Y on predictors (X, Z) has conditional mean function based on a linear combination of (X, Z). We generalize these models to have a nonparametric component, replacing the linear combination α
T
0
X + β
T
0
Z by η
0
(α
T
0
X) + β
T
0
Z, where η
0
(·) is an unknown function. We call these generalized partially linear single-index models (GPLSIM). The models include the "single-index" models, which have β
0
= 0. Using local linear methods, we propose estimates of the unknown parameters (α
0
, β
0
) and the unknown function η
0
(·) and obtain their asymptotic distributions. Examples illustrate the models and the proposed estimation methodology. |
| doi_str_mv | 10.1080/01621459.1997.10474001 |
| format | Article |
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T
0
X + β
T
0
Z by η
0
(α
T
0
X) + β
T
0
Z, where η
0
(·) is an unknown function. We call these generalized partially linear single-index models (GPLSIM). The models include the "single-index" models, which have β
0
= 0. Using local linear methods, we propose estimates of the unknown parameters (α
0
, β
0
) and the unknown function η
0
(·) and obtain their asymptotic distributions. Examples illustrate the models and the proposed estimation methodology.</description><identifier>ISSN: 0162-1459</identifier><identifier>EISSN: 1537-274X</identifier><identifier>DOI: 10.1080/01621459.1997.10474001</identifier><identifier>CODEN: JSTNAL</identifier><language>eng</language><publisher>Alexandria, VA: Taylor & Francis Group</publisher><subject>Asymptotic theory ; Estimation methods ; Estimation theory ; Estimators ; Exact sciences and technology ; Generalized linear models ; Kernel regression ; Linear inference, regression ; Linear models ; Linear regression ; Local estimation ; Local polynomial regression ; Logistics ; Mathematical models ; Mathematics ; Modeling ; Nonparametric inference ; Nonparametric models ; Nonparametric regression ; Parametric models ; Probability and statistics ; Quasi-likelihood ; Regression analysis ; Sciences and techniques of general use ; Statistical methods ; Statistics ; Theory and Methods ; Wands</subject><ispartof>Journal of the American Statistical Association, 1997-06, Vol.92 (438), p.477-489</ispartof><rights>Copyright Taylor & Francis Group, LLC 1997</rights><rights>Copyright 1997 American Statistical Association</rights><rights>1997 INIST-CNRS</rights><rights>Copyright American Statistical Association Jun 1997</rights><lds50>peer_reviewed</lds50><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c436t-8610c0f04c4894c06ae2f77b7cd832184494d3be858e172f0155981fb8c2db363</citedby><cites>FETCH-LOGICAL-c436t-8610c0f04c4894c06ae2f77b7cd832184494d3be858e172f0155981fb8c2db363</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktopdf>$$Uhttps://www.jstor.org/stable/pdf/2965697$$EPDF$$P50$$Gjstor$$H</linktopdf><linktohtml>$$Uhttps://www.jstor.org/stable/2965697$$EHTML$$P50$$Gjstor$$H</linktohtml><link.rule.ids>314,780,784,803,832,27869,27924,27925,58017,58021,58250,58254,59647,60436</link.rule.ids><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=2812651$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>Carroll, R. J.</creatorcontrib><creatorcontrib>Fan, Jianqing</creatorcontrib><creatorcontrib>Gijbels, Irène</creatorcontrib><creatorcontrib>Wand, M. P.</creatorcontrib><title>Generalized Partially Linear Single-Index Models</title><title>Journal of the American Statistical Association</title><description>The typical generalized linear model for a regression of a response Y on predictors (X, Z) has conditional mean function based on a linear combination of (X, Z). We generalize these models to have a nonparametric component, replacing the linear combination α
T
0
X + β
T
0
Z by η
0
(α
T
0
X) + β
T
0
Z, where η
0
(·) is an unknown function. We call these generalized partially linear single-index models (GPLSIM). The models include the "single-index" models, which have β
0
= 0. Using local linear methods, we propose estimates of the unknown parameters (α
0
, β
0
) and the unknown function η
0
(·) and obtain their asymptotic distributions. Examples illustrate the models and the proposed estimation methodology.</description><subject>Asymptotic theory</subject><subject>Estimation methods</subject><subject>Estimation theory</subject><subject>Estimators</subject><subject>Exact sciences and technology</subject><subject>Generalized linear models</subject><subject>Kernel regression</subject><subject>Linear inference, regression</subject><subject>Linear models</subject><subject>Linear regression</subject><subject>Local estimation</subject><subject>Local polynomial regression</subject><subject>Logistics</subject><subject>Mathematical models</subject><subject>Mathematics</subject><subject>Modeling</subject><subject>Nonparametric inference</subject><subject>Nonparametric models</subject><subject>Nonparametric regression</subject><subject>Parametric models</subject><subject>Probability and statistics</subject><subject>Quasi-likelihood</subject><subject>Regression analysis</subject><subject>Sciences and techniques of general use</subject><subject>Statistical methods</subject><subject>Statistics</subject><subject>Theory and Methods</subject><subject>Wands</subject><issn>0162-1459</issn><issn>1537-274X</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1997</creationdate><recordtype>article</recordtype><sourceid>K30</sourceid><sourceid>8G5</sourceid><sourceid>ABUWG</sourceid><sourceid>AFKRA</sourceid><sourceid>AZQEC</sourceid><sourceid>BENPR</sourceid><sourceid>CCPQU</sourceid><sourceid>DWQXO</sourceid><sourceid>GNUQQ</sourceid><sourceid>GUQSH</sourceid><sourceid>M2O</sourceid><recordid>eNqF0F1LwzAUBuAgCs7pX5Ch4l1nvpNeDtE5mCio4F1I01Q6smYmHTp_vSnbZAhibgLhOS8nLwCnCA4RlPAKIo4RZfkQ5blIT1RQCNEe6CFGRIYFfd0HvQ5lnToERzHOYDpCyh6AY9vYoF39ZcvBow5trZ1bDaZ1Y3UYPNXNm7PZpCnt5-Del9bFY3BQaRftyebug5fbm-fru2z6MJ5cj6aZoYS3meQIGlhBaqjMqYFcW1wJUQhTSoKRpDSnJSmsZNIigSuIGMslqgppcFkQTvrgcp27CP59aWOr5nU01jndWL-MikjGIZcdPPsFZ34ZmrSbSn-XmFCGEjr_C6HUFyEkwaT4WpngYwy2UotQz3VYKQRV17Xadq26rtW26zR4sYnX0WhXBd2YOv5MY4kwZztsFlsfdsMxgULhnDOei8RGa1Y3lQ9z_eGDK1WrV86HbTT5Z6NvWd2aOg</recordid><startdate>19970601</startdate><enddate>19970601</enddate><creator>Carroll, R. 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J. ; Fan, Jianqing ; Gijbels, Irène ; Wand, M. P.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c436t-8610c0f04c4894c06ae2f77b7cd832184494d3be858e172f0155981fb8c2db363</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1997</creationdate><topic>Asymptotic theory</topic><topic>Estimation methods</topic><topic>Estimation theory</topic><topic>Estimators</topic><topic>Exact sciences and technology</topic><topic>Generalized linear models</topic><topic>Kernel regression</topic><topic>Linear inference, regression</topic><topic>Linear models</topic><topic>Linear regression</topic><topic>Local estimation</topic><topic>Local polynomial regression</topic><topic>Logistics</topic><topic>Mathematical models</topic><topic>Mathematics</topic><topic>Modeling</topic><topic>Nonparametric inference</topic><topic>Nonparametric models</topic><topic>Nonparametric regression</topic><topic>Parametric models</topic><topic>Probability and statistics</topic><topic>Quasi-likelihood</topic><topic>Regression analysis</topic><topic>Sciences and techniques of general use</topic><topic>Statistical methods</topic><topic>Statistics</topic><topic>Theory and Methods</topic><topic>Wands</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Carroll, R. 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J.</au><au>Fan, Jianqing</au><au>Gijbels, Irène</au><au>Wand, M. P.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Generalized Partially Linear Single-Index Models</atitle><jtitle>Journal of the American Statistical Association</jtitle><date>1997-06-01</date><risdate>1997</risdate><volume>92</volume><issue>438</issue><spage>477</spage><epage>489</epage><pages>477-489</pages><issn>0162-1459</issn><eissn>1537-274X</eissn><coden>JSTNAL</coden><abstract>The typical generalized linear model for a regression of a response Y on predictors (X, Z) has conditional mean function based on a linear combination of (X, Z). We generalize these models to have a nonparametric component, replacing the linear combination α
T
0
X + β
T
0
Z by η
0
(α
T
0
X) + β
T
0
Z, where η
0
(·) is an unknown function. We call these generalized partially linear single-index models (GPLSIM). The models include the "single-index" models, which have β
0
= 0. Using local linear methods, we propose estimates of the unknown parameters (α
0
, β
0
) and the unknown function η
0
(·) and obtain their asymptotic distributions. Examples illustrate the models and the proposed estimation methodology.</abstract><cop>Alexandria, VA</cop><pub>Taylor & Francis Group</pub><doi>10.1080/01621459.1997.10474001</doi><tpages>13</tpages></addata></record> |
| fulltext | fulltext |
| identifier | ISSN: 0162-1459 |
| ispartof | Journal of the American Statistical Association, 1997-06, Vol.92 (438), p.477-489 |
| issn | 0162-1459 1537-274X |
| language | eng |
| recordid | cdi_proquest_journals_274823451 |
| source | Periodicals Index Online; JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; Access via Taylor & Francis |
| subjects | Asymptotic theory Estimation methods Estimation theory Estimators Exact sciences and technology Generalized linear models Kernel regression Linear inference, regression Linear models Linear regression Local estimation Local polynomial regression Logistics Mathematical models Mathematics Modeling Nonparametric inference Nonparametric models Nonparametric regression Parametric models Probability and statistics Quasi-likelihood Regression analysis Sciences and techniques of general use Statistical methods Statistics Theory and Methods Wands |
| title | Generalized Partially Linear Single-Index Models |
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