Asymptotic normality for the estimator of non parametric regression model under ϕ-mixing errors

ABSTRACT

In this article, by using the Rosenthal-type inequality and the Bernstein's big-block and small-block procedure, we establish the asymptotic normality for the estimators of non parametric regression model based on ϕ-mixing errors. The result obtained in the article generalizes some corresponding ones for some dependent random variables.

KEYWORDS:

• Asymptotic normality
• Non parametric regression model
• ϕ-Mixing random variables

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G20

Acknowledgments

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