Semiparametric regression models with errors in variables

In this dissertation, a method has been proposed to be used for the partially linear model, a semiparametric regression model, when variables are measured with errors and the densities of these errors are unknown. Firstly parametric, nonparametric and semiparametric regression models, smoothing in regression, roughness penalty approach and smoothing methods in nonparametric regression are introduced. Then, as a nonparametric and semiparametric regression method when variables are measured with an error that has ''known'' density, nonparametric regression with errors in variables models, semiparametric regression models with measurement error in the nonparametric part and semiparametric regression models with errors in all variables are introduced. Finally, as a nonparametric regression method when variables are measured with an error that has ''unknown'' density, nonparametric regression with errors in variables models are introduced and semiparametric regression models with measurement error in the nonparametric part and semiparametric regression models with errors in all variables which are obtained according to this method and seen as an alternative to the kernel deconvolution techniques have been developed. These estimators' asymptotic normality properties are analyzed to observe whether they fit a normal distribution around the parameters they converge when the sample size of estimators obtained by these methods n goes to infinity. The finite sample properties of estimators were investigated by Monte Carlo simulation approach.