Invariance principles and almost sure central limit theorem for the error variance estimator in linear models

ABSTRACT

In this article, we establish the invariance principles for the error variance estimator in linear models, which weaken the conditions for the errors in Chen (1980) from finite fourth moment to infinite fourth moment. Furthermore, the almost sure central limit theorem of the error variance estimator is also obtained under the assumption for the errors of infinite fourth moment.

KEYWORDS:

• Invariance principles
• Almost sure central limit theorem
• error variance estimator
• linear models.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60F17

Acknowledgments

The authors are very grateful to the referees for their valuable reports which improved the presentation of this work.

Funding

This work is supported by IRTSTHN (14IRTSTHN023), NSFC (11471104), and Outstanding Youth Talent of Henan Normal University.