Large sample theory in a semiparametric partially linear errors-in-variables models - Hua Liang; Wolfgang Härdle; Raymond J. Carroll (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 1997)
We consider the partially linear model relating a response Y to predictors (X,T) with mean function XT ß + 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 ß 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 ß is shown to be consistent and its asymptotic distribution theory is derived. Consistent standard error estimates using sandwich-type ideas are also developed.
urn:nbn:de:kobv:11-10064133
Keywords: 330; Measurement Error; Errors-in-Variables; Functional Relations; Non-parametric Likelihood; Orthogonal Regression; Partially Linear Model; Semiparametric Models; Structural Relations