Exact and adaptive prediction intervals for order statistics

Abstract

We construct exact prediction intervals for future order statistics based on a random sample from a given family of distributions with unknown location and scale parameters. In the one sample problem, only a specified number of the first order statistics are available. In the two sample problem, predicitons are made for a second independent sample. We also propose an adaptive two stage procedure when the distribution is unknown. First the data are used to select a distribution and then a prediction interval for that distribution is constructed. We show that the adaptive procedure provides protection against model misspecification