Some convergence properties for partial sums of widely orthant dependent random variables and their statistical applications

Abstract

In this paper, we present the $$L_p$$ convergence for partial sums $$S_n=\sum _{k=1}^nX_k$$ under the Cesaro uniform integrability condition and the complete convergence for the maximum of $$S_n$$ for sequences of widely orthant dependent random variables $$\{X_n,n\ge 1\}.$$ Some of the results extend the corresponding ones in reference. As applications, we get the complete consistency and the strong consistency for the estimator in a nonparametric regression model.