## The Annals of Statistics

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

### The Quadratic Loss of Isotonic Regression Under Normality

#### 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

**Permanent link to this document**

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**

links.jstor.org

**Subjects**

Primary: 62F10: Point estimation

Secondary: 62A10

**Keywords**

Isotonic regression maximum likelihood estimator mean square error

#### Citation

Lee, Chu-In Charles. The Quadratic Loss of Isotonic Regression Under Normality. Ann. Statist. 9 (1981), no. 3, 686--688. doi:10.1214/aos/1176345475. https://projecteuclid.org/euclid.aos/1176345475