The asymptotic normality of the linear weighted estimator in nonparametric regression models

Consider the following nonparametric regression model:where x(ni) are known fixed design points from for some positive integer d > 1, g( center dot ) is an unknown regression function defined on A and epsilon(ni) are random errors. Under some suitable conditions, the asymptotic normality of the linear weighted estimator of g in the nonparametric regression model based on rho-mixing errors is established. The key techniques used in the paper are the Rosenthal type inequality and the Bernstein's bigblock and small-block procedure. The result obtained in the paper generalizes the corresponding ones for some dependent sequences.