Smoothed weighted empirical likelihood ratio confidence intervals for quantiles

    Authors

    J. J. Ren

    Comments

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    Abbreviated Journal Title

    Bernoulli

    Keywords

    bootstrap; doubly censored data; empirical likelihood; interval censored; data; partly interval censored data; right censored data; DOUBLY CENSORED-DATA; SELF-CONSISTENT ESTIMATORS; FAILURE TIME MODEL; GOODNESS-OF-FIT; NONPARAMETRIC-ESTIMATION; ASYMPTOTIC PROPERTIES; BOOTSTRAP; TESTS; CHOICE; Statistics & Probability

    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-likelillood 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.

    Journal Title

    Bernoulli

    Volume

    14

    Issue/Number

    3

    Publication Date

    1-1-2008

    Document Type

    Article

    Language

    English

    First Page

    725

    Last Page

    748

    WOS Identifier

    WOS:000264166300007

    ISSN

    1350-7265

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