Moment inequalities for \(m\)-negatively associated random variables and their applications
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.
\(m\)-negatively associated random variables
scientific article; zbMATH DE number 6818159
scientific article