Limiting behaviour for arrays of rowwise widely orthant dependent random variables under conditions of R − h-integrability and its applications

Abstract

ABSTRACTIn this paper, we mainly study the convergence, complete convergence and complete moment convergence for arrays of rowwise widely orthant dependent (WOD, for short) random variables under some conditions of R-h-integrability. The results in this paper generalize and improve the corresponding ones of Sung et al., Weak laws of large numbers for arrays under a condition of uniform integrability, Journal of the Korean Mathematical Society 45 (2008), pp. 289–300, Wang and Hu, Weak laws of large numbers for arrays of dependent random variables, Stochastics: An International Journal of Probability and Stochastic Processes 86 (2014), pp. 759–775, and Wu et al., Limiting behaviour for arrays of rowwise END random variables under conditions of h-integrability, Stochastics: An International Journal of Probability and Stochastic Processes 87 (2014), pp. 409–423. As applications of the complete convergence that we established, we present some results on complete consistency for the estimator in a nonparametric regression model based on WOD errors.