In this paper, we propose empirical likelihood methods based on influence function and Jackknife techniques to construct confidence intervals for quantile medical costs with censored data. We show that the influence function-based empirical log-likelihood ratio statistic for the quantile medical cost has a standard Chi-square distribution as its asymptotic distribution. Simulation studies are conducted to compare coverage probabilities and interval lengths of the proposed empirical likelihood confidence intervals with the existing normal approximation-based confidence intervals for quantile medical costs. The proposed methods are observed to have better finite-sample performances than existing methods. The new methods are also illustrated through a real example.
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