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 onρ~-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.

Complete convergence and complete moment convergence for extended negatively dependent random variables

“…The following one is a fundamental inequality for stochastic domination. For the proof, one can refer to Wu [22], or Wang et al ( [16], [17]). Lemma 2.9.…”

The consistency for the estimator of nonparametric regression model based on martingale difference errors

“…generalized the results of Liang and Jing (2005) for negatively associated sequences to the case negatively orthant dependent sequences. Wang et al (2012b) investigated the complete consistency for the estimator of nonparametric regression models based onρ-mixing sequences. Shen (2013a) studied the strong consistency of estimator of fixed design regression model under widely dependent random variables, Wang et al (2014a) investigated complete convergence for arrays of row-wise negatively superadditive-dependent random variables and its applications.…”

Bernstein-Type Inequality for Widely Dependent Sequence and Its Application to Nonparametric Regression Models

“…Yang et al [12] generalized the results of Liang and Jing [11] for negatively associated sequences to the case of negatively orthant dependent sequences and obtained the strong consistency for the estimator of the nonparametric regression models based on negatively orthant dependent errors. Wang et al [13] studied the complete consistency of the estimator of nonparametric regression models based oñ -mixing sequences, and so forth. The main purpose of this paper is to investigate the strong consistency for the estimator of the nonparametric regression models based on widely dependent random variables, which contains independent random variables, negatively associated random variables, negatively orthant dependent random variables, extended negatively orthant dependent random variables, and some positively dependent random variables as specials cases.…”