Complete convergence for weighted sums of NSD random variables and its application in the EV regression model

<Para ID="Par1">In this paper, some basic properties for negatively superadditive-dependent (NSD, in short) random variables are presented, such as the Rosenthal-type inequality and the Kolmogorov-type exponential inequality. Using these properties, we further study the complete convergence for weighted sums of NSD random variables, which generalizes and improves some corresponding ones for independent random variables and negatively associated random variables. Some sufficient conditions to prove the complete convergence for weighted sums of NSD random variables are provided. As an application, the complete consistency of LS estimators in the EV regression model with NSD errors is investigated under mild conditions, which generalizes and improves the corresponding one for negatively associated random variables. Copyright Sociedad de Estadística e Investigación Operativa 2015