This paper investigates the distribution-free outer confidence interval for the quantile interval introduced by Wilks. Besides exact expressions and a recurrence formula some bounds are derived for the probability of correct coverage of the quantile interval which improve bounds known up to now, and which are tested in several examples. Asymptotic approximations are discussed and applications of the developed methods to other statistics based on order statistics are indicated.
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Reiss et al. (1976) studied this question.
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