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THE BEST LEAST ABSOLUTE DEVIATIONS LINE – PROPERTIES AND TWO EFFICIENT METHODS FOR ITS DERIVATION

Part of: Linear inference, regression Numerical approximation and computational geometry Probabilistic methods, simulation and stochastic differential equations Operations research and management science Functional-differential and differential-difference equations

Published online by Cambridge University Press:  01 October 2008

KRISTIAN SABO  and
RUDOLF SCITOVSKI
KRISTIAN SABO
Affiliation:
Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, HR-31000 Osijek, Croatia (email: ksabo@mathos.hr)
RUDOLF SCITOVSKI*
Affiliation:
Department of Mathematics, University of Osijek, Trg Ljudevita Gaja 6, HR-31000 Osijek, Croatia (email: scitowsk@mathos.hr)
*
✉For correspondence; e-mail: scitowsk@mathos.hr
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Abstract

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Given a set of points in the plane, the problem of existence and finding the least absolute deviations line is considered. The most important properties are stated and proved and two efficient methods for finding the best least absolute deviations line are proposed. Compared to other known methods, our proposed methods proved to be considerably more efficient.

Keywords

least absolute deviationsLADl1-norm approximationweighted median problem

MSC classification

Secondary: 65D10: Smoothing, curve fitting 65C20: Models, numerical methods 62J05: Linear regression 90C56: Derivative-free methods and methods using generalized derivatives 90B85: Continuous location 34K29: Inverse problems
Type
Research Article
Information
The ANZIAM Journal , Volume 50 , Issue 2 , October 2008 , pp. 185 - 198
Copyright
Copyright © Australian Mathematical Society 2009

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