Estimation of Quantiles of Location-Scale Distributions Based on Two or Three Order Statistics

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Abstract
Linear asymptotically unbiased estimators of ξ quantiles, x ξ 0 < ξ < 1, of location-scale distributions are considered. These are based on two or three order statistics suitably selected in a neighborhood of the sample quantile X (N), N = [nξ] + 1, where n is the sample size. The estimators are easy to calculate and are substantially more efficient than the nonparametric estimator ξ = X (N). The estimators are tabulated for selected values of ξ for the normal and extreme value (Gumbel) distributions. Also given are the asymptotic relative efficiencies of these estimators when compared with the maximum likelihood estimator of x ξ based on all n observations.

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