On the Central Limit Theorem for a Conditional Mode Estimator of a Randomly Censored Time Series

Abstract

In this article, we consider a kernel estimator of the conditional density function from which we derive an estimator of the conditional mode. We address the case of a randomly right-censored model when the data exhibit some kind of dependency. The conditional mode estimator is defined as the random variable that maximizes the conditional density estimator. Under classical conditions we establish a central-limit theorem for this estimator. We carry out a simulation study to illustrate our results.

• Primary 62G20
• 62G05

• Asymptotic distribution
• Censored data
• Conditional mode
• Kaplan–Meier estimator
• Kernel estimator
• Strong mixing condition