# SFB 303 Discussion Paper No. A-567

**Author**: Li, Z., Chai, G. and Xu, K.

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

**Abstract**: 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 be avoided. 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.

**Keywords**: wavelet, semiparametric model, nonlinear wavelet estimator, income distribution

**JEL-Classification-Number**: C14, D31

**Creation-Date**: December, 1997

**URL:**
../1997/a/bonnsfa567.pdf
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