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 T fi + g(T ) when the X's are measured with additive error. The semiparametric likelihood estimate of Severini and Staniswalis (1994) leads to biased estimates of both the parameter fi and the function g(\Delta) 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 fi is shown to be consistent and its asymptotic distribution theory is derived. Consistent standard error estimates using sandwich--type ideas are also developed. Key Words and Phrases: Errors-in-Variables; Functional Relations; Measurement Error; Nonparametric Likelihood; Orthogonal Regression; Partially Linear Model; Semiparametric Models; Structural Relations. Short title: Partially Linear Models and Measurement Error. AMS 1991 subject classification: Primary: 62J99, 62H12,..