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On a Sufficient Condition and a Necessary Condition for L1 Estimation

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  • V. A. Sposito
  • W. C. Smith

Abstract

Published results by Appa and Smith (1973) establish necessary conditions for fitting a linear model to a set of points via the criterion of least sum of absolute deviations (called the L1 criterion). This note identifies a sufficient condition, and a necessary condition when the number of observations is odd, that can be utilized in combination with the necessary conditions of Appa and Smith to identify an optimal plane under L1 from a finite set of planes.

Suggested Citation

  • V. A. Sposito & W. C. Smith, 1976. "On a Sufficient Condition and a Necessary Condition for L1 Estimation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 25(2), pages 154-157, June.
    • Handle: RePEc:bla:jorssc:v:25:y:1976:i:2:p:154-157
    DOI: 10.2307/2346684
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