# SFB 303 Discussion Paper No. A-554

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

**Title**: Note on error density estimation in nonparametric regression and application to income data

**Abstract**: From last decade, nonparametric statistical methods have been widely used in econometrics, since they over versatility and exibility in estimation and forecasting-one needs not to specify functional forms. Consider a nonparametric regression model yi = m(xi ) + ei;i= 1;2;...n, assume m(...) unknown and to be estimated based on (x 0i ; yi ) which are i.i.d. observations of random variable (X 0; Y). Here assume that i.i.d. errors ei come from an unknown density function f(e). This paper will give some extension asymptotic properties of a nonparametric estimator ^fn (e) off(e). Application will go to the estimation of income distribution of United Kingdom which has recently been considerable popular. Personal income observations will come.
from U.K. Family Expenditure Survey from 1968 to 1987. Sampling size for each year is around 7000.

**Keywords**: Nonparametric regression; Error density; Asymptotic normality; Smoothing parameter; Income distribution.

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

**Creation-Date**: August, 1997

**URL**: ../1997/a/bonnsfa554.pdf"
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