Consistency properties for the wavelet estimator in nonparametric regression model with dependent errors

Abstract

Abstract In this paper, we establish the pth mean consistency, complete consistency, and the rate of complete consistency for the wavelet estimator in a nonparametric regression model with m-extended negatively dependent random errors. We show that the best rates can be nearly O ( n − 1 / 3 ) $O(n^{-1/3})$ under some general conditions. The results obtained in the paper markedly improve and extend some corresponding ones to a much more general setting.

Keywords

• Mean consistency
• Complete consistency
• Rate of consistency
• Nonparametric regression model
• m-extended negative dependence