Calculating nonparametric confidence intervals for quantiles using fractional order statistics

Alan Hutson

Journal of Applied Statistics, 1999, vol. 26, issue 3, 343-353

Abstract: In this paper, we provide an easy-to-program algorithm for constructing the preselected 100(1 - alpha)% nonparametric confidence interval for an arbitrary quantile, such as the median or quartile, by approximating the distribution of the linear interpolation estimator of the quantile function Q L ( u ) = (1 - epsilon) X \[ n u ] + epsilon X \[ n u ] + 1 with the distribution of the fractional order statistic Q I ( u ) = Xn u , as defined by Stigler, where n = n + 1 and \[ . ] denotes the floor function. A simulation study verifies the accuracy of the coverage probabilities. An application to the extreme-value problem in flood data analysis in hydrology is illustrated.

Date: 1999
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DOI: 10.1080/02664769922458

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