Smoothed weighted empirical likelihood ratio confidence intervals for quantiles

TL;DR

This paper develops smoothed weighted empirical likelihood ratio confidence intervals for quantiles applicable to various censored data types, improving accuracy and interval length compared to existing methods.

Contribution

It introduces a unified framework for constructing WELRCI for different censored data types, including smoothing techniques and theoretical accuracy guarantees.

Findings

WELRCI achieves at least first-order coverage accuracy.

Smoothing results in shorter confidence intervals with comparable coverage.

WELRCI performs favorably in simulation studies for various censored data types.

Abstract

Thus far, likelihood-based interval estimates for quantiles have not been studied in the literature on interval censored case 2 data and partly interval censored data, and, in this context, the use of smoothing has not been considered for any type of censored data. This article constructs smoothed weighted empirical likelihood ratio confidence intervals (WELRCI) for quantiles in a unified framework for various types of censored data, including right censored data, doubly censored data, interval censored data and partly interval censored data. The fourth order expansion of the weighted empirical log-likelihood ratio is derived and the theoretical coverage accuracy equation for the proposed WELRCI is established, which generally guarantees at least `first order' accuracy. In particular, for right censored data, we show that the coverage accuracy is at least $O(n^{-1/2})$ and our simulation studies show that in comparison with empirical likelihood-based methods, the smoothing used in WELRCI generally provides a shorter confidence interval with comparable coverage accuracy. For interval censored data, it is interesting to find that with an adjusted rate $n^{-1/3}$, the weighted empirical log-likelihood ratio has an asymptotic distribution completely different from that obtained by the empirical likelihood approach and the resulting WELRCI perform favorably in the available comparison simulation studies.