Consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors

In this paper, we establish the strong consistency and complete consistency of the Priestley–Chao estimator in nonparametric regression model with widely orthant dependent errors under some general conditions. We also obtain the rates of strong consistency and complete consistency. We show that the rates can approximate to O(n−1/3)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$O(n^{-1/3})$\end{document} under appropriate conditions. The results obtained in the paper improve or extend the corresponding ones to widely orthant dependent assumptions.