## The Annals of Statistics

### The Quadratic Loss of Isotonic Regression Under Normality

Chu-In Charles Lee

#### Abstract

The maximum likelihood estimator $\hat{\mu}$ of a nondecreasing regression function has been studied in detail in the literature. However, little is known about its quadratic loss pointwise. This paper shows that the mean square error of $\hat{\mu}_i$ is less than that of the usual estimator $\bar{X}_i$ for each $i$ when $\bar{X}_1,\cdots, \bar{X}_k$ are independent normal variates.

#### Article information

Source
Ann. Statist., Volume 9, Number 3 (1981), 686-688.

Dates
First available in Project Euclid: 12 April 2007

https://projecteuclid.org/euclid.aos/1176345475

Digital Object Identifier
doi:10.1214/aos/1176345475

Mathematical Reviews number (MathSciNet)
MR615447

Zentralblatt MATH identifier
0477.62015

JSTOR