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

Kelly, Robert E.

Ann. Stat. 17, No. 2, 937-940 (1989).

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

Keywords:

loss function; maximum likelihood; order restriction; stochastic; ordering; ordered means; independent normal random variables; absolute error; isotonic regression estimator