Estimation of Varying Coefficient Models with Measurement Error

We propose a semi-parametric estimator for varying coefficient models when the regressors in the nonparametric component are measured with error. Varying coefficient models are an extension of other popular semiparametric models, including partially linear and nonparametric additive models, and deliver an attractive solution to the curse-of-dimensionality. We use deconvolution kernel estimation in a two-step procedure and show that the estimator is consistent and asymptotically normally distributed. We do not assume that we know the distribution of the measurement error a priori, nor do we assume that the error is symmetrically distributed. Instead, we suppose we have access to a repeated measurement of the noisy regressor and use the approach of Li and Vuong (1998) based on Kotlarski�s (1967) identity. We show that the convergence rate of the estimator is significantly reduced when the distribution of the measurement error is assumed unknown and possibly asymmetric. Finally, we study the small sample behavior of our estimator in a simulation study.