Asymptotic properties of wavelet-based estimator in nonparametric regression model with weakly dependent processes
Xingcai Zhou, Jin‐Guan Lin, Chang-Ming Yin · Journal of Inequalities and Applications · 2013
In this paper, we consider a nonparametric regression model with replicated observations based on the φ -mixing and the ρ -mixing error’s structures respectively, for exhibiting dependence among the units. The wavelet procedures are developed to estimate the regression function. Under suitable conditions, we obtain expansions for the bias and the variance of wavelet estimator, prove the moment consistency, the strong consistency, the strong convergence rate of it, and establish the asymptotic normality of wavelet estimator.