## Stochastic reduction of loss in estimating normal means by isotonic regression.(English)Zbl 0673.62021

Summary: Consider the problem of estimating the ordered means $$\mu_ 1\leq \mu_ 2\leq...\leq \mu_ k$$ of independent normal random variables, $$Y_ 1,Y_ 2,...,Y_ k$$. It is shown that the absolute error of each component $${\hat \mu}{}_ i$$ of the isotonic regression estimator is stochastically smaller than that of the usual estimator $$Y_ i$$. Thus $${\hat \mu}{}_ i$$ is superior to $$Y_ i$$ under any nonconstant loss which is a nondecreasing function of absolute error.

### MSC:

 62F10 Point estimation 62C99 Statistical decision theory 60E15 Inequalities; stochastic orderings
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