BIAS COMPARISON NADARAYA WATSON AND LOCALLY LINEAR KERNEL ESTIMATOR OF NONPARAMETRIC REGRESSION

Abstract

dth: 0px; "> Given a data set (xi , yi ) and connecting between xi and yi be assumed to follow
nonparametric regression model :
yi  m(xi ) ï€«ï¥ i , i  1,2,...,n.
Regresssion curve of m be assumed is an unknown form and ï¥ i , is an error term in the
observations are IID with mean 0 and finite variance ï³ 2.
In this paper propose to exist mean conditional estimators with employ the local
polinomial method which polinomial degree p = 0 will be formed the Nadaraya-Watson
estimator and p = 1 to exist the Locally Linear estimator. Furthemore, with the same method
also be existed the comparison both bias and variance. Kernel estimator will be applied of
the Canadian Males Data by Murphy and Welch (1990).

Key words: Nonparametric estimation, weighted least square, Local polinomial