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Consider the problem of estimating the ordered means ₁ ₂ ₖ of independent normal random variables, Y₁, Y₂, , Yₖ. It is shown that the absolute error of each component ᵢ of the isotonic regression estimator is stochastically smaller than that of the usual estimator Yᵢ. Thus ᵢ is superior to Yᵢ under any nonconstant loss which is a nondecreasing function of absolute error.
Robert E. Kelly (Thu,) studied this question.