## Generalized Partially Linear Single-Index Models (1998)

Venue: | Journal of the American Statistical Association |

Citations: | 63 - 24 self |

### BibTeX

@ARTICLE{Carroll98generalizedpartially,

author = {R. J. Carroll and Jianqing Fan and Irène Gijbels and M.P. Wand},

title = {Generalized Partially Linear Single-Index Models},

journal = {Journal of the American Statistical Association},

year = {1998},

volume = {92},

pages = {477--489}

}

### Years of Citing Articles

### OpenURL

### Abstract

The typical generalized linear model for a regression of a response Y on predictors (X; Z) has conditional mean function based upon a linear combination of (X; Z). We generalize these models to have a nonparametric component, replacing the linear combination T 0 X + T 0 Z by 0 ( T 0 X) + T 0 Z, 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, estimates of the unknown parameters ( 0 ; 0 ) and the unknown function 0 ( ) are proposed, and their asymptotic distributions obtained. Examples illustrate the models and the proposed estimation methodology.