Mathematical Programming

, Volume 5, Issue 1, pp 73–87 | Cite as

On L1 and Chebyshev estimation

  • Gautam Appa
  • Cyril Smith
Article
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Abstract

The problem considered here is that of fitting a linear function to a set of points. The criterion normally used for this is least squares. We consider two alternatives, viz., least sum of absolute deviations (called the L1 criterion) and the least maximum absolute deviation (called the Chebyshev criterion). Each of these criteria give rise to a linear program. We develop some theoretical properties of the solutions and in the light of these, examine the suitability of these criteria for linear estimation. Some of the estimates obtained by using them are shown to be counter-intuitive.

Keywords

Linear Function Mathematical Method Absolute Deviation Linear Estimation Theoretical Property 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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Copyright information

© The Mathematical Programming Society 1973

Authors and Affiliations

  • Gautam Appa
    • 1
  • Cyril Smith
    • 2
  1. 1.Middlesex Polytechnic at EnfieldMiddlesexEngland
  2. 2.London School of EconomicsLondonEngland

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