Asymptotic linear prediction of extreme order statistics
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We consider the problem of predicting thesth order statistic using the lowestr order statistics from a large sample of sizen under the assumption that the sample minimum, appropriately normalized, has a non-degenerate limit distribution asn→∞. Assumingr, s fixed andn→∞ we obtain asymptotically best linear unbiased as well as asymptotically best linear invariant predictors of thesth order statistic.
Key wordsExtreme-value distributions best linear unbiased predictor best linear invariant predictors
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