Annals of the Institute of Statistical Mathematics

, Volume 49, Issue 4, pp 761–775

Choosing a Linear Model with a Random Number of Change-Points and Outliers

  • Henri Caussinus
  • Faouzi Lyazrhi

DOI: 10.1023/A:1003230713770

Cite this article as:
Caussinus, H. & Lyazrhi, F. Annals of the Institute of Statistical Mathematics (1997) 49: 761. doi:10.1023/A:1003230713770


The problem of determining a normal linear model with possible perturbations, viz. change-points and outliers, is formulated as a problem of testing multiple hypotheses, and a Bayes invariant optimal multi-decision procedure is provided for detecting at most k (k > 1) such perturbations. The asymptotic form of the procedure is a penalized log-likelihood procedure which does not depend on the loss function nor on the prior distribution of the shifts under fairly mild assumptions. The term which penalizes too large a number of changes (or outliers) arises mainly from realistic assumptions about their occurrence. It is different from the term which appears in Akaike‘s or Schwarz‘ criteria, although it is of the same order as the latter. Some concrete numerical examples are analyzed.

Akaike‘s criterionBayes decision procedurechange-pointinvariancemaximal invariantoutliersregression analysisSchwarz‘ criterion

Copyright information

© The Institute of Statistical Mathematics 1997

Authors and Affiliations

  • Henri Caussinus
    • 1
  • Faouzi Lyazrhi
    • 1
  1. 1.Laboratoire de Statistique et Probabilités, UMR-CNRS 5583Université Paul Sabatier, 118Toulouse CedexFrance