Stochastic Reduction of Loss in Estimating Normal Means by Isotonic Regression
The Annals of Statistics · 1989 · Volume 17 · Issue 2
Abstract
Consider the problem of estimating the ordered means $\mu_1 \leq \mu_2 \leq \cdots \leq \mu_k$ of independent normal random variables, $Y_1, Y_2, \cdots, Y_k$. 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.
Keywords
60E15, 62C99, 62E99, 62F10, isotonic regression, loss function, maximum likelihood, order restriction, stochastic ordering
Enable JavaScript for citation tools and additional paper interactions.