Minimum Kolmogorov distance estimates of parameters and parametrized distributions

L. Györfi, I. Vajda, E. Van Der Meulen

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Minimum Kolmogorov distance estimates of arbitrary parameters are considered They are shown to be strongly consistent if the parameter space metric is topologically weaker than the metric induced by the Kolmogorov distance of distributions from the statistical model. If the parameter space metric can be locally uniformly upper-bounded by the induced metric then these estimates are shown to be consistent of order n-1/2. Similar results are proved for minimum Kolmogorov distance estimates of densities from parametrized families where the consistency is considered in the L1-norm. The presented conditions for the existence, consistency, and consistency of order n-1/2 are much weaker than those established in the literature for estimates with similar properties. It is shown that these assumptions are satisfied e.g. by all location and scale models with parent distributions different from Dirac, and by all standard exponential models.

Original languageEnglish
Pages (from-to)237-255
Number of pages19
JournalMetrika
Volume43
Issue number1
Publication statusPublished - Jan 1 1996

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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