Abstract:
We consider the nonparametric regression model =
g(
Xi)+
εi, where the residual
εi is a stationary
φ-mixed process with unknown common density function
f(
x),
g(
x) = E(
Y|
X =
x) is the unknown regression function. In this paper, first we define the residuals estimates based on the nonparametric estimator \hatg_n(x) for
g(
x), then we construct the estimate \widehatf_n(x) for
f(
x)on the basis of the residuals, the pointwise weak and strong consistency as well as the uniform strong consistency of \widehatf_n(x) are estabilished under some suitable conditions.