On the convergence rates of kernel estimator and hazard estimator for widely dependent samples
In this paper, we establish a Bernstein-type inequality for widely orthant dependent random variables, and obtain the rates of strong convergence for kernel estimators of density and hazard functions, under some suitable conditions.
Basic renewal theorems for random walks with widely dependent increments
Abstract In this paper, we derive some basic renewal theorems for random walks with widely dependent increments, which contain some common negatively dependent random variables (r.v.s.), some positively dependent r.v.s. and some others. For this purpose, we investigate uniform integrability for related counting processes and the strong law of large numbers for the widely dependent r.v.s.
On complete convergence of weighted sums for arrays of rowwise extended negatively dependent random variables
Let be an array of rowwise extended negatively dependent (END) random variables. The complete convergence for weighted sums of arrays of rowwise END random variables is studied, which complements and improves the corresponding result of Baek and Park [2] and Baek et al. [1]. As an application, the Baum–Katz type result for arrays of rowwise END random variables is obtained.