Strong consistency of non parametric kernel regression estimator for strong mixing samples

ABSTRACT

For α-mixing samples, we study Priestley–Chao kernel estimator for non parametric regression model. By using the moment inequality and the exponential inequality, the strong consistency and the uniformly strong consistency of the estimator are obtained for some weak conditions.

KEYWORDS:

• α-Mixing samples
• non parametric regression
• Priestley–Chao estimator
• strong consistency.

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G08
• 62E20

Acknowledgments

The authors are grateful to the editor and referee for their suggestions that greatly improved the article. This research was supported by the Natural Science Foundation of China [grant number 11461009], the Natural Science Foundation of Hainan [grant number 117173] and the Scientific Research Project of the Guangxi Colleges and Universities [grant number KY2015YB345].