Nonlinear wavelet smoothing of error distribution in a semi-parametric model

Consider a semiparametric model yi = xi' beta + g(ti )+ei; i = 1;2..., n, error ei are i.i.d. random variables from unknown distribution f(e). In this paper, we propose a nonlinear wavelet estimator ^f(e) of f(e) based on residuals ê =yi - ^yi here restriction of uniformly continuous on f(e) might beavoided. Following the way used in Hall et al (1995), we provide an asymptotic formula for the mean integrated squared error of ^ f(e), some numerical examples will be given in the end of the paper.