Open Access
August 2008 Smoothed weighted empirical likelihood ratio confidence intervals for quantiles
Jian-Jian Ren
Bernoulli 14(3): 725-748 (August 2008). DOI: 10.3150/08-BEJ129

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.

Citation

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Jian-Jian Ren. "Smoothed weighted empirical likelihood ratio confidence intervals for quantiles." Bernoulli 14 (3) 725 - 748, August 2008. https://doi.org/10.3150/08-BEJ129

Information

Published: August 2008
First available in Project Euclid: 25 August 2008

zbMATH: 1155.62033
MathSciNet: MR2537809
Digital Object Identifier: 10.3150/08-BEJ129

Keywords: bootstrap , doubly censored data , empirical likelihood , interval censored data , partly interval censored data , Right censored data

Rights: Copyright © 2008 Bernoulli Society for Mathematical Statistics and Probability

Vol.14 • No. 3 • August 2008
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