Estimation 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(inverted perpendicular)beta + g(T) when the X's are measured with additive error. The semiparametric likelihood estimate of Severini and Staniswalis leads to biased estimates of both the parameter beta and the function g((.))when measurement error is ignored. We derive a simple modification of their estimator which is a semiparametric version of the usual parametric correction for attenuation. The resulting estimator of beta is shown to be consistent and its asymptotic distribution theory is derived. Consistent standard error estimates using sandwich-type ideas are also developed.