Strong asymptotic properties of kernel smoothing estimation for NA random variables with right censoring

Abstract

Most studies for negatively associated (NA) random variables consider the complete-data situation, which is actually a relatively ideal condition in practice. The article relaxes this condition to the incomplete-data setting and considers kernel smoothing density and hazard function estimation in the presence of right censoring based on the Kaplan–Meier estimator. We establish the strong asymptotic properties for these two estimators to assess their asymptotic behavior and justify their practical use.

Keywords:

• Kaplan-Meier estimator
• kernel smoothing estimator
• NA random variable
• right censoring

2020 Mathematics Subject Classification:

• 62G05

Acknowledgments

We are grateful to the anonymous reviewer for valuable comments and suggestions which greatly improved this paper.

Correction Statement

This article has been corrected with minor changes. These changes do not impact the academic content of the article.

Additional information

Funding

The work is supported by The National Social Science Fund of China (20XTJ003).