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

In this paper, we study 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 under some appropriate conditions, which extend and improve the corresponding ones in classical probability space to the case of sub-linear expectation space. And we obtain a strong law of large numbers for the randomly weighted sums of arrays of rowwise widely negative dependent random variables. As applications of our main results, we not only present a result on the complete consistency for the weighted estimator in a nonparametric regression model, but also obtain the complete consistency for the least squares estimators in errors-in-variables regression models based on widely negative dependent errors under sub-linear expectations. We perform some numerical simulations to verify the validity of the theoretical results and a real example is analysed for illustration.