Generalized partially linear single index model with measurement error, instruments and binary response

Abstract

Partially linear generalized single index models are widely used and have attracted much attention in the literature. However, when the covariates are subject to measurement error, the problem is much less studied. On the other hand, instrumental variables are important elements in studying many errors-in-variables problems. We use the relation between the unobservable variables and the instruments to devise consistent estimators for partially linear generalized single index models with binary response. We establish the consistency, asymptotic normality of the estimator and illustrate the numerical performance of the method through simulation studies and a data example. Despite the connection to (Scand. J. Statist. 42 (2015) 104–117) in its general layout, the mathematical derivations are much more challenging in the context studied here.