# Strong Asymptotic Properties of Kernel Smoothing Estimation for NA Random Variables with Right Censoring

## TL;DR

This paper extends kernel smoothing estimation methods to negatively associated random variables with right censoring, establishing their strong asymptotic properties to support practical applications in incomplete-data scenarios.

## Contribution

It introduces the first strong asymptotic analysis of kernel estimators for NA variables under right censoring, relaxing previous ideal assumptions.

## Key findings

- Established strong asymptotic properties of kernel density estimators
- Validated the use of Kaplan-Meier based estimators in NA contexts
- Provided theoretical justification for practical kernel smoothing in censored data

## Abstract

Most studies for negatively associated (NA) random variables consider the complete-data situation, which is actually a relatively ideal condition in practice. The paper 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.