Generalized partially linear single-index models Academic Article

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 T0X + T0Z by 0(T0X) + T0Z, where 0() is an unknown function. We call these generalized partially linear single-index models (GPLSIM). The models include the single-index models, which have 0 = 0. Using local linear methods, we propose estimates of the unknown parameters (0, 0) and the unknown function 0() and obtain their asymptotic distributions. Examples illustrate the models and the proposed estimation methodology. 1997 Taylor & Francis Group, LLC.

authors

• Carroll, Raymond

published proceedings

• JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION

altmetric score

• 3

author list (cited authors)

• Carroll, R. J., Fan, J. Q., Gijbels, I., & Wand, M. P.

citation count

• 598

complete list of authors

• Carroll, RJ||Fan, JQ||Gijbels, I||Wand, MP

publication date

• June 1997

publisher

• Taylor & Francis  Publisher

published in

• JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION  Journal

keywords

• Asymptotic Theory
• Generalized Linear Models
• Kernel Regression
• Local Estimation
• Local Polynomial Regression
• Nonparametric Regression
• Quasi-likelihood

Digital Object Identifier (DOI)

• 10.2307/2965697

start page

• 477

end page

• 489

volume

• 92

issue

• 438

URL

• http%3A%2F%2Fdx.doi.org%2F10.1080%2F01621459.1997.10474001