On the rate of convergence in the strong law of large numbers for negatively orthant-dependent random variables

ABSTRACT

In this paper, we study the complete convergence and complete moment convergence for negatively orthant-dependent random variables. Especially, we obtain the Hsu–Robbins-type theorem for negatively orthant-dependent random variables. Our results generalize the corresponding ones for independent random variables.

KEYWORDS:

• Complete convergence
• Hsu–Robbins-type theorem
• NOD random variables

MATHEMATICS SUBJECT CLASSIFICATION:

• 60F15

Acknowledgments

The authors are most grateful to the Editor-in-Chief N. Balakrishnan and anonymous referee for careful reading of the manuscript and valuable suggestions which helped in improving an earlier version of this paper.

Funding

Supported by the National Natural Science Foundation of China (11501004, 11501005, 11526033), the Natural Science Foundation of Anhui Province (1508085J06), the Provincial Natural Science Research Project of Anhui Colleges (KJ2015A018), the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005), the Quality Engineering Project of Anhui Province (2015jyxm045) and the Quality Improvement Project for Undergraduate Education of Anhui University (ZLTS2015035).