Complete and complete moment convergence with applications to the EV regression models

ABSTRACT

In this paper, the complete convergence and complete moment convergence for arrays of rowwise m-extended negatively dependent (m-END, for short) random variables are established. As an application, the Marcinkiewicz-Zygmund type strong law of large numbers for m-END random variables is also achieved. By using the results that we established, we further investigate the strong consistency of the least square estimator in the simple linear errors-in-variables models, and provide some simulations to verify the validity of our theoretical results.

KEYWORDS:

• Complete convergence
• complete moment convergence
• m-extended negatively dependent random variables
• simple linear errors-in-variables models
• strong consistency

MATHEMATICAL SUBJECT CLASSIFICATIONS:

• 60F15
• 62F12

Acknowledgements

The authors are most grateful to the editor and anonymous referees for carefully reading the manuscript and for valuable suggestions which helped in improving an earlier version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Supported by the National Natural Science Foundation of China (11671012, 11871072), the Natural Science Foundation of Anhui Province (1508085J06), the Key Projects for Academic Talent of Anhui Province (gxbjZD2016005) and the Project on Reserve Candidates for Academic and Technical Leaders of Anhui Province (2017H123).