Strong Consistency of Wavelet Estimator for Biased Nonparametric Regression Function Under Strong Mixing

Abstract

This paper focuses on the function estimation problem in nonparametric regression model based on biased samples under strong mixing. We propose a wavelet estimator by using wavelet kernel and investigate the consistency properties of the wavelet estimator. The mean consistency, strong consistency and convergence rate are obtained and the convergence rate is similar as that of wavelet estimator in the standard nonparametric model even although with the presence of bias and strong mixing dependence.