The Annals of Statistics

On Boscovich's Estimator

Roger Koenker and Gilbert Bassett

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Abstract

Boscovich's (1757) proposal to estimate the parameters of a linear model by minimizing the sum of absolute deviations subject to the constraint that the mean residual be zero is considered. The asymptotic theory of the estimator confirms a remark of Edgeworth who called it a "remarkable hybrid" between $\mathscr{l}_1$ and $\mathscr{l}_2$ methods.

Article information

Source
Ann. Statist., Volume 13, Number 4 (1985), 1625-1628.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349759

Digital Object Identifier
doi:10.1214/aos/1176349759

Mathematical Reviews number (MathSciNet)
MR811514

Zentralblatt MATH identifier
0612.62041

JSTOR
links.jstor.org

Subjects
Primary: 62F12: Asymptotic properties of estimators
Secondary: 62J07: Ridge regression; shrinkage estimators

Keywords
Least absolute error estimators linear models asymptotic theory

Citation

Koenker, Roger; Bassett, Gilbert. On Boscovich's Estimator. Ann. Statist. 13 (1985), no. 4, 1625--1628. doi:10.1214/aos/1176349759. https://projecteuclid.org/euclid.aos/1176349759


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