GENERALIZED PARTIALLY LINEAR SINGLE-INDEX MODELS

Citation
Rj. Carroll et al., GENERALIZED PARTIALLY LINEAR SINGLE-INDEX MODELS, Journal of the American Statistical Association, 92(438), 1997, pp. 477-489
Citations number
28
Categorie Soggetti
Statistic & Probability","Statistic & Probability
Volume
92
Issue
438
Year of publication
1997
Pages
477 - 489
Database
ISI
SICI code
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 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.