Semiparametric EIV Regression Model with Unknown Errors in all Variables

Abstract

This paper develops a method for semiparametric partially linear regression model when all variables measured with errors whose densities are unknown. Identification is achieved using the availability of two errorcontaminated measurements of the independent variables. This method is likened to kernel deconvolution method which relies on the assumption that measurement errors densities are known. However with this deconvolution method, convergence rates are very slow. Hence, estimating a regression function with super smooth errors is extremely difficult and in literature the authors only have studied the case that the errors are ordinary smooth. We could tackle this problem with the Fourier representation of the Nadaraya-Watson estimator, because this method can handle both of super smooth and ordinary smooth distributions. In literature studying asymptotic normality also has difficulty because of the same smoothing problem. With this study we could manage to show asymptotic normality of parametric part. Monte Carlo experiments demonstrated the performances of 𝛽̂ and 𝑔̂𝑛 (𝑡) in the application part.