The Strong Consistency of M Estimator in a Linear Model for Negatively Dependent Random Samples

Abstract

The strong consistency of M estimators of the regression parameters in linear models for negatively dependent random errors under some mild conditions is established, which is an essential improvement on the relevant results in the literature on the moment conditions and dependent errors. Especially, Theorems 1 and 2 of Wu (2006) are not only extended to the case of negatively dependent random errors, but also are improved essentially on the moment conditions.

Keywords:

• Linear model
• M estimator
• Moment condition
• Negatively dependent random error
• Strong consistency

Mathematics Subject Classification:

• 62F12

Acknowledgments

We are very grateful to the referees and the Editors for their valuable comments and some helpful suggestions that improved the clarity and readability of the article.

Supported by the National Natural Science Foundation of China (11061012), the Support Program of the New Century Guangxi China Ten-hundred-thousand Talents Project (2005214), and the Guangxi China Science Foundation (0991081 and 2010GXNSFA013120).