On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression models

In this paper, some probability inequalities and moment inequalities for widely orthant-dependent (WOD, in short) random variables are presented, especially the Marcinkiewicz–Zygmund type inequality and Rosenthal type inequality. By using these inequalities, we further study the complete convergence for weighted sums of arrays of row-wise WOD random variables and give some special cases, which extend some corresponding ones for dependent sequences. As applications, we present some sufficient conditions to prove the complete consistency for the estimator of nonparametric regression model based on WOD errors by using the complete convergence that we established. At last, the choice of the fixed design points and the weight functions for the nearest neighbor estimates is proposed. Our results generalize some known results for independent random variables and some dependent random variables. Copyright Sociedad de Estadística e Investigación Operativa 2014