The Annals of Statistics

The Quadratic Loss of Isotonic Regression Under Normality

Chu-In Charles Lee

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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


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