Wavelet estimation of semiparametric errors in variables model

Abstract

Most of the work on wavelet estimation when the variables are measured with errors have centered around nonparametric approaches which cause curse of dimensionality. In this paper it is aimed to avoid this complexity using wavelet semiparametric errors in variables regression model. Using theoretical arguments for nonparametric wavelet estimation a wavelet approach is represented to estimate partially linear errors in variables model which is a semiparametric model when explanatory variable of nonparametric part has measurement error. Assuming that the measurement error has a known distribution we derive an estimator of the linear parts' parameter. In simulation study derived method is compared with no measurement error case.