Optimal Progressive Type-II Censoring Schemes for Non-Parametric Confidence Intervals of Quantiles

Abstract

<p> In this work, optimal censoring schemes are investigated for the non-parametric confidence intervals of population quantiles under progressive Type-II right censoring. The proposed inference can be universally applied to any probability distributions for continuous random variables. By using the interval mass as an optimality criterion, the optimization process is also independent of the actual observed values from a sample as long as the initial sample size n and the number of observations m are predetermined. This study is based on the fact that each (uncensored) order statistic observed from progressive Type-II censoring can be represented as a mixture of underlying ordinary order statistics with exactly known weights [11, 12]. Using several sample sizes combined with various degrees of censoring, the results of the optimization are tabulated here for a wide range of quantiles with selected levels of significance (i.e., α = 0.01, 0.05, 0.10). With the optimality criterion under consideration, the efficiencies of the worst progressive Type-II censoring scheme and ordinary Type-II censoring scheme are also examined in comparison with the best censoring scheme obtained for a given quantile with fixed n and m.</p>