Large Sample Theory in a Semiparametric Partially Linear Errors-in-variables Model

We consider the partially linear model relating a response Y to predictors (X;T ) with mean function X + g(T ) when the X 's are measured with additive error. The semiparametric likelihood estimate of Severini and Staniswallis (1994) leads to biased estimates of both the parameter and the function g( ) when measurement error is ignored. We derive a simple modi cation of their estimator which is a semiparametric version of the usual parametric correction for attenuation. The resulting estimator of is shown to be consistent and its asymptotic distribution theory is derived. Consistent standard error estimates using sandwich{type ideas are also developed.