Asymptotic Confidence Intervals for the Length of the Shortt under RandomCensoring

摘要

A shortt of a one dimensional probability distribution is defined to be aninterval which has at least probability t and minimal length. The length of a shortt and its obvious estimator are significant measures of scale of a distribution and the corresponding random sample, respectively. In this note, a non-parametric asymptotic confidence interval for the length of the (uniqueness is assumed) shortt is established in the random censorship from the right model. The estimator of the length of the shortt is based on the product-limit (PL) estimator of the unknown distribution function. The proof of the result mainly follows from an appropriate combination of the Glivenko-Cantelli theorem and the functional central limit theorem for the PL estimator.