# Nonparametric estimation of the conditional density function with right-censored and dependent data

## TL;DR

This paper develops and analyzes nonparametric estimators for the conditional density function using right-censored, dependent data, extending existing results to stationary alpha-mixing sequences and validating performance through simulations.

## Contribution

It extends the asymptotic normality and consistency results of local linear estimators to dependent data under alpha-mixing conditions, relaxing previous independence assumptions.

## Key findings

- Asymptotic normality of estimators established
- Consistency of estimators proven under alpha-mixing
- Finite sample performance demonstrated via simulations

## Abstract

In this paper, we study the local constant and the local linear estimators of the conditional density function with right-censored data which exhibit some type of dependence. It is assumed that the observations form a stationary $\alpha-$mixing sequence. The asymptotic normality of the two estimators is established, which combined with the condition that $\lim\limits_{n\rightarrow\infty}nh_nb_n=\infty$ implies the consistency of the two estimators and can be employed to construct confidence intervals for the conditional density function. The result on the local linear estimator of the conditional density function in Kim et al. (2010) is relaxed from the i.i.d. assumption to the $\alpha-$mixing setting, and the result on the local linear estimator of the conditional density function in Spierdijk (2008) is relaxed from the $\rho$-mixing assumption to the $\alpha-$mixing setting. Finite sample behavior of the estimators is investigated by simulations.