Uniform strong consistency of histogram density estimation for dependent process

ABSTRACT

Histogram density estimator is very intuitive and easy to compute and has been widely adopted. Especially in today's big data environment, people pay more attention to the computational cost and are more willing to choose estimators with less to compute. And so, many scholars have been interested in the various estimates based on the histogram technique. Under strong mixing process, this article studies the uniform strong consistency of histogram density estimator and the convergence rate. Our conditions on the mixing coefficient and the bin width are very mild.

KEYWORDS:

• Histogram density estimator
• Strong mixing process
• Uniform strong consistency

MATHEMATICS SUBJECT CLASSIFICATION:

• 62G05
• 62G20

Acknowledgments

The author is grateful to the referees for their valuable suggestions.

Funding

This research is supported by the National Science Foundation of China (11461009), the Natural Science Foundation of Guangxi (2011GXNSFA018133), and the Scientific research project of the Guangxi Colleges and Universities (KY2015YB345).