Generalized Partially Linear Single-Index Models

Carroll, RJ; Fan, J; Gijbels, I; Wand, MP

Generalized Partially Linear Single-Index Models

Carroll, RJ

Fan, J Gijbels, I Wand, MP

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Publication Type:: Journal Article
Citation:: Journal of the American Statistical Association, 1997, 92 (438), pp. 477 - 489
Issue Date:: 1997-06-01

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Field	Value	Language
dc.contributor.author	Carroll, RJ https://orcid.org/0000-0002-5465-9682	en_US
dc.contributor.author	Fan, J	en_US
dc.contributor.author	Gijbels, I	en_US
dc.contributor.author	Wand, MP https://orcid.org/0000-0003-2555-896X	en_US
dc.date.issued	1997-06-01	en_US
dc.identifier.citation	Journal of the American Statistical Association, 1997, 92 (438), pp. 477 - 489	en_US
dc.identifier.issn	0162-1459	en_US
dc.identifier.uri	http://hdl.handle.net/10453/13008
dc.description.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 αT0X + βT0Z by η0(αT0X) + βT0Z, where η0(·) is an unknown function. We call these generalized partially linear single-index models (GPLSIM). The models include the “single-index” models, which have β0 = 0. Using local linear methods, we propose estimates of the unknown parameters (α0, β0) and the unknown function η0(·) and obtain their asymptotic distributions. Examples illustrate the models and the proposed estimation methodology. © 1997 Taylor & Francis Group, LLC.	en_US
dc.relation.ispartof	Journal of the American Statistical Association	en_US
dc.relation.isbasedon	10.1080/01621459.1997.10474001	en_US
dc.subject.classification	Statistics & Probability	en_US
dc.title	Generalized Partially Linear Single-Index Models	en_US
dc.type	Journal Article
utslib.citation.volume	438	en_US
utslib.citation.volume	92	en_US
utslib.for	0104 Statistics	en_US
utslib.for	1403 Econometrics	en_US
utslib.for	1603 Demography	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Science
pubs.organisational-group	/University of Technology Sydney/Faculty of Science/School of Mathematical and Physical Sciences
utslib.copyright.status	closed_access
pubs.issue	438	en_US
pubs.publication-status	Published	en_US
pubs.volume	92	en_US

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 αT0X + βT0Z by η0(αT0X) + βT0Z, where η0(·) is an unknown function. We call these generalized partially linear single-index models (GPLSIM). The models include the “single-index” models, which have β0 = 0. Using local linear methods, we propose estimates of the unknown parameters (α0, β0) and the unknown function η0(·) and obtain their asymptotic distributions. Examples illustrate the models and the proposed estimation methodology. © 1997 Taylor & Francis Group, LLC.

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http://hdl.handle.net/10453/13008