Summary
This paper considers the prediction of the sample mean by extreme order statistics when the population distribution is known. The predictor and its mean square error are found. The problem is studied in details for the normal model.
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Pham, T.D., Tran, L.T. Predicting the sample mean by extreme order statistics. Metrika 36, 117–125 (1989). https://doi.org/10.1007/BF02614083
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DOI: https://doi.org/10.1007/BF02614083