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November 1997 The Gaussian hare and the Laplacian tortoise: computability of squared-error versus absolute-error estimators
Stephen Portnoy, Roger Koenker
Statist. Sci. 12(4): 279-300 (November 1997). DOI: 10.1214/ss/1030037960

Abstract

Since the time of Gauss, it has been generally accepted that 2-methods of combining observations by minimizing sums of squared errors have significant computational advantages over earlier 1-methods based on minimization of absolute errors advocated by Boscovich, Laplace and others. However, 1-methods are known to have significant robustness advantages over 2-methods in many applications, and related quantile regression methods provide a useful, complementary approach to classical least-squares estimation of statistical models. Combining recent advances in interior point methods for solving linear programs with a new statistical preprocessing approach for 1-type problems, we obtain a 10- to 100-fold improvement in computational speeds over current (simplex-based) 1-algorithms in large problems, demonstrating that 1-methods can be made competitive with 2-methods in terms of computational speed throughout the entire range of problem sizes. Formal complexity results suggest that 1-regression can be made faster than least-squares regression for n sufficiently large and p modest.

Citation

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Stephen Portnoy. Roger Koenker. "The Gaussian hare and the Laplacian tortoise: computability of squared-error versus absolute-error estimators." Statist. Sci. 12 (4) 279 - 300, November 1997. https://doi.org/10.1214/ss/1030037960

Information

Published: November 1997
First available in Project Euclid: 22 August 2002

zbMATH: 0955.62608
MathSciNet: MR1619189
Digital Object Identifier: 10.1214/ss/1030037960

Keywords: , , interior point , least absolute deviations , linear programming , median , regression quantiles , simplex method , simultaneous confidence bands , statistical preprocessing

Rights: Copyright © 1997 Institute of Mathematical Statistics

Vol.12 • No. 4 • November 1997
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