Complete Consistency of the Estimator of Nonparametric Regression Models Based on ρ ~ -Mixing Sequences

Abstract

We study the complete consistency for estimator of nonparametric regression model based on $\stackrel{\mathbf{~}}{\mathit{\rho }}$-mixing sequences by using the classical Rosenthal-type inequality and the truncated method. As an application, the complete consistency for the nearest neighbor estimator is obtained.