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Abstract We consider an estimation problem when only the k largest observations of a sample of size n are available. It is assumed that the underlying distribution function F belongs to the domain of attraction of a known extreme-value distribution and that k remains fixed as n → ∞. We present estimators for the location and scale parameters and for p-quantiles of F, where p is of the form 1 — c/n (c fixed). These estimators are either asymptotically maximum likelihood or minimum variance.
Ishay Weissman (Fri,) studied this question.