## Bernoulli

• Bernoulli
• Volume 14, Number 3 (2008), 725-748.

### Smoothed weighted empirical likelihood ratio confidence intervals for quantiles

Jian-Jian Ren

#### 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.

#### Article information

Source
Bernoulli, Volume 14, Number 3 (2008), 725-748.

Dates
First available in Project Euclid: 25 August 2008

https://projecteuclid.org/euclid.bj/1219669627

Digital Object Identifier
doi:10.3150/08-BEJ129

Mathematical Reviews number (MathSciNet)
MR2537809

Zentralblatt MATH identifier
1155.62033

#### Citation

Ren, Jian-Jian. Smoothed weighted empirical likelihood ratio confidence intervals for quantiles. Bernoulli 14 (2008), no. 3, 725--748. doi:10.3150/08-BEJ129. https://projecteuclid.org/euclid.bj/1219669627

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