Moment inequalities for \(m\)-negatively associated random variables and their applications
type: Item
instance of: scholarly article
title: Moment inequalities for \(m\)-negatively associated random variables and their applications
zbMATH Open document ID: 1387.60058
author: Aiting Shen
author: Yu Zhang
author: Benqiong Xiao
author: Andrei Volodin
published in: Statistical Papers
publication date: 2017-12-13T00:00:00Z
review text: The authors study properties of sequences \(\{X_n: n \geq 1\}\) of random variables possessing the property of being \(m\)-negatively associated (\(m\)-NA) for some fixed integer \(m \geq 1\). In particular, they establish inequalities of Marcinkiewicz-Zygmund type and Rosenthal type, respectively, for such sequences. As corollaries, they derive a Khinchin-Kolmogorov type convergence theorem and the three series theorem for \(m\)-NA random variables. Two statistical applications of the main results are considered, namely, large deviation properties of least squares estimators in nonlinear regression models involving \(m\)-NA error terms, and strong consistency of least squares estimators in multiple linear regression, again under the \(m\)-NA assumption regarding the error terms.
reviewed by: Thorsten Dickhaus
Mathematics Subject Classification ID: 60F15
Mathematics Subject Classification ID: 62J02
Mathematics Subject Classification ID: 62F12
zbMATH DE Number: 6818159
zbMATH Keywords: Marcinkiewicz-Zygmund-type inequality
zbMATH Keywords: multiple linear regression models
zbMATH Keywords: nonlinear regression
zbMATH Keywords: Rosenthal-type inequality
zbMATH Keywords: \(m\)-negatively associated random variables
MaRDI profile type: Publication
full work available at URL: s00362-015-0731-x
OpenAlex ID: W2495985019
cites work: Q3924997
cites work: Convergence systems and strong consistency of least squares estimates in regression models
cites work: On Complete Convergence for Arrays of Row-Wise Negatively Associated Random Variables
cites work: The rate of convergence for the least squares estimator in nonlinear regression model with dependent errors.
cites work: Consistency for the least squares estimator in nonlinear regression model
cites work: On complete convergence for arrays of rowwise \(m\)-negatively associated random variables
cites work: An Asymptotic Expansion for the Distribution of the Least Squares Estimator of the Non-Linear Regression Parameter
cites work: Q4335415
cites work: Q4692964
cites work: Asymptotic Properties of Non-Linear Least Squares Estimators
cites work: Negative association of random variables, with applications
cites work: Strong convergence for weighted sums of negatively associated arrays
cites work: The Bahadur representation for sample quantiles under negatively associated sequence
cites work: The Consistency of Nonlinear Regressions
cites work: A note on the almost sure convergence of sums of negatively dependent random variables
cites work: The rate of convergence of the least squares estimator in a non-linear regression model with dependent errors
cites work: Q4048357
cites work: A comparison theorem on moment inequalities between negatively associated and independent random variables
cites work: On the strong convergence for weighted sums of random variables
cites work: Complete convergence and complete moment convergence for a class of random variables
cites work: Weak laws of large numbers for arrays of dependent random variables
cites work: Strong Limit Theorems for Weighted Sums of Negatively Associated Random Variables
cites work: Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications
cites work: On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models
cites work: Large deviation for a least squares estimator in a nonlinear regression model
cites work: Complete convergence of weighted sums under negative dependence
DOI: 10.1007/S00362-015-0731-X
description: scientific article; zbMATH DE number 6818159