The strong consistency of M-estimates in linear models with extended negatively dependent errors

ABSTRACT

In this paper, we first establish the strong convergence for weighted sums of extended negatively dependent (END) random variables. Based on the strong convergence and Bernstein inequality, we obtain the strong consistency of M-estimates of the regression parameters in a linear model for END random errors under some mild moment conditions. The results generalize and improve the ones obtained in the literature to the case of END random errors.

KEYWORDS:

• Extended negatively dependent random variables
• linear model
• M-estimate
• strong consistency.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62F12
• 62J05

Acknowledgments

The authors thank the Editor in Chief Prof. N. Balakrishnan and two anonymous referees for their helpful comments and valuable suggestions that greatly improved the paper.

Funding

This work is supported by the National Natural Science Foundation of China (11526033, 11501004, 11501005, 11671012), the Natural Science Foundation of Anhui Province (1608085QA02, 1408085QA02), the Science Fund for Distinguished Young Scholars of Anhui Province (1508085J06), and Introduction Projects of Anhui University Academic and Technology Leaders.