The convergence properties for randomly weighted sums of widely negative dependent random variables under sub-linear expectations with related statistical applications (Q6648831)

Sublinear expectation is a functional with the properties of monotonicity, constant preservation, subadditivity, and positive homogeneity. The paper studies the complete convergence and complete moment convergence for randomly weighted sums of arrays of rowwise widely negative dependent random variables in sub-linear expectation space. The results extend those previously established in probability theory. One of the results obtained is the strong law of large numbers. A result on the complete consistency for the weighted estimator in a nonparametric regression model is complemented by the established complete consistency for the least squares estimators in errors-in-variables regression models. The article contains some numerical simulations.