Law of the single logarithm for randomly weighted sums of dependent sequences and an application

Abstract

In this work, the law of the single logarithm for randomly weighted sums of widely orthant dependent random variables was studied, which improved and generalized some corresponding results in the literature. As an application, the rate of complete convergence for random weighting estimation with widely orthant dependent samples was obtained under general assumptions. Some numerical analyses were also conducted to confirm the theoretical results.

Keywords

• law of the single logarithm
• randomly weighted sums
• complete convergence
• random weighting estimation
• widely orthant dependent