Consistent order estimation and minimal penalties

Elisabeth Gassiat, Ramon Van Handel

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


Consider an i.i.d. sequence of random variables whose distribution lies in one of the nested families of models , . The smallest index such that contains is called themodel order. The aim of this paper is to explore the consistency properties of penalized likelihood model order estimators such as Bayesian information criterion. We show in a general setting that the minimal strongly consistent penalty is of order , where is a dimensional quantity. In contrast to previous work, an a priori upper bound on the model order is not assumed. The results rely on a sharp characterization of the pathwise fluctuations of the generalized likelihood ratio statistic under entropy assumptions on the model classes. Our results are applied to the geometrically complex problem of locationmixture order estimation, which is widely used but poorly understood.

Original languageEnglish (US)
Article number6317186
Pages (from-to)1115-1128
Number of pages14
JournalIEEE Transactions on Information Theory
Issue number2
StatePublished - 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


  • Consistent order estimation
  • location mixtures
  • penalized likelihood
  • uniform law of iterated logarithm


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