The Annals of Statistics

Improved Confidence Sets for the Coefficients of a Linear Model with Spherically Symmetric Errors

Jiunn Tzon Hwang and Jeesen Chen

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Abstract

Under the assumption of normal errors, confidence spheres for $p(p \geq 3)$ coefficients of a linear model centered at the positive part James-Stein estimators were recently proved, by Hwang and Casella, to dominate the usual confidence set with the same radius. In this paper, the same domination results are established under various spherically symmetric distributions. These distributions include uniform distributions, double exponential distributions, and multivariate $t$ distributions.

Article information

Source
Ann. Statist., Volume 14, Number 2 (1986), 444-460.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349932

Digital Object Identifier
doi:10.1214/aos/1176349932

Mathematical Reviews number (MathSciNet)
MR840508

Zentralblatt MATH identifier
0601.62048

JSTOR
links.jstor.org

Subjects
Primary: 62F25: Tolerance and confidence regions
Secondary: 62F35: Robustness and adaptive procedures 62J07: Ridge regression; shrinkage estimators 62C20: Minimax procedures

Keywords
Coverage probability uniform distribution double exponential distribution multivariate $t$ distribution spherically symmetric distributions

Citation

Hwang, Jiunn Tzon; Chen, Jeesen. Improved Confidence Sets for the Coefficients of a Linear Model with Spherically Symmetric Errors. Ann. Statist. 14 (1986), no. 2, 444--460. doi:10.1214/aos/1176349932. https://projecteuclid.org/euclid.aos/1176349932


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