The typical generalized linear model for a regression of a response Y
on predictors (X, Z) has conditional mean function based on a linear c
ombination of (X, Z). We generalize these models to have a nonparametr
ic component, replacing the linear combination alpha(0)(T)X + beta(0)(
T)Z by eta(0)(alpha(0)(T)X) + beta(0)(T)Z, where eta(0)(.) is an unkno
wn function: We call these generalized partially lineal single-index m
odels (GPLSIM). The models include the ''single-index'' models, which
have beta(0) = 0. Using local linear methods, we propose estimates of
the unknown parameters (alpha(0), beta(0)) and the unknown function et
a(0)(.) and obtain their asymptotic distributions. Examples illustrate
the models and the proposed estimation methodology.