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 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.