The Annals of Statistics

Algorithms in Order Restricted Statistical Inference and the Cauchy Mean Value Property

Tim Robertson and F. T. Wright

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Abstract

Most algorithms in order restricted statistical inference express the estimates in terms of certain summary statistics computed from pooled samples. These algorithms may or may not yield optimal estimates depending on whether or not the Cauchy mean value property holds strictly for the summary statistics. In this paper a minimum lower sets algorithm, which holds generally, is described and used to prove the optimality of estimates described by a max-min formula.

Article information

Source
Ann. Statist., Volume 8, Number 3 (1980), 645-651.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345014

Digital Object Identifier
doi:10.1214/aos/1176345014

Mathematical Reviews number (MathSciNet)
MR568726

Zentralblatt MATH identifier
0441.62038

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 62F10: Point estimation

Keywords
Optimality $L_p$ problems Cauchy mean value function computation algorithms isotonic regression

Citation

Robertson, Tim; Wright, F. T. Algorithms in Order Restricted Statistical Inference and the Cauchy Mean Value Property. Ann. Statist. 8 (1980), no. 3, 645--651. doi:10.1214/aos/1176345014. https://projecteuclid.org/euclid.aos/1176345014


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