Asymptotic linear prediction of extreme order statistics (Q802246)

We consider the problem of predicting the s th order statistic using the lowest r order statistics from a large sample of size n under the assumption that the sample minimum, appropriately normalized, has a non- degenerate limit distribution as \(n\to \infty\). Assuming r, s fixed and \(n\to \infty\) we obtain asymptotically best linear unbiased as well as asymptotically best linear invariant predictors of the s th order statistic.