LAD in Multi-Way Tables

  • Peter Bloomfield
  • William L. Steiger
Part of the Progress in Probability and Statistics book series (PRPR, volume 6)


An important special case of the general linear model discussed in Chapters 1 and 2 is when the data fall into a multi-way table. The simplest case is the one-way layout, where the data are organized into c cells, with observations yjk, 1 ≤ k ≤ nj, in the jth cell, 1 ≤ j ≤ c.


Median Polish Rational Entry Important Special Case Column Median Half Step 
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  1. 1.
    Emerson and Hoaglin (1983) discuss the relationship between LAD fitting and median polish. They also discuss “polishing” tables using other measures of location.Google Scholar
  2. 2.
    Kemperman (1983) discusses fitting to tables by other discrete Lp criteria, p > 1, but focuses mainly on the case p = 1. He also discusses general ideas in the construction of an algorithm like median polish that would be guaranteed to converge to a LAD fit.Google Scholar
  3. 3.
    Siegel (1983) has a graph-theoretic construction for moving from a polished table to a LAD fit by forcing certain extra residuals to zero.Google Scholar
  4. 4.
    Theorem 4.2 is new, as is the procedure, modified median polish, to which it refers.Google Scholar

Copyright information

© Birkhäuser Boston, Inc. 1983

Authors and Affiliations

  • Peter Bloomfield
    • 1
  • William L. Steiger
    • 2
  1. 1.Department of StatisticsNorth Carolina State UnversityRaleighUSA
  2. 2.Department of Computer ScienceRutgers UniversityNew BrunswickUSA

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