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We consider the partially linear model relating a response Y to predictors (X, T) with mean function X T β + 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 β 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 β is shown to be consistent and its asymptotic distribution theory is derived. Consistent standard error estimates using sandwich-type ideas are also developed.

Estimation in a semiparametric partially linear errors-in-variables model