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1996-1997 | 24 | 4 | 415-423
Tytuł artykułu

Information-type divergence when the likelihood ratios are bounded

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The so-called ϕ-divergence is an important characteristic describing "dissimilarity" of two probability distributions. Many traditional measures of separation used in mathematical statistics and information theory, some of which are mentioned in the note, correspond to particular choices of this divergence. An upper bound on a ϕ-divergence between two probability distributions is derived when the likelihood ratio is bounded. The usefulness of this sharp bound is illustrated by several examples of familiar ϕ-divergences. An extension of this inequality to ϕ-divergences between a finite number of probability distributions with pairwise bounded likelihood ratios is also given.
Rocznik
Tom
24
Numer
4
Strony
415-423
Opis fizyczny
Daty
wydano
1997
otrzymano
1996-09-16
poprawiono
1996-12-10
Twórcy
  • Department of Mathematics and Statistics, University of Maryland at Baltimore County, 1000 Hilltop Circle, Baltimore, Maryland 21250, U.S.A.
Bibliografia
  • [1] D. A. Bloch and L. E. Moses, Nonoptimally weighted least squares, Amer. Statist. 42 (1988), 50-53.
  • [2] T. M. Cover, M. A. Freedman and M. E. Hellman, Optimal finite memory learning algorithms for the finite sample problem, Information Control 30 (1976), 49-85.
  • [3] T. M. Cover and J. A. Thomas, Elements of Information Theory, Wiley, New York, 1991.
  • [4] L. Devroy, Non-Uniform Random Variate Generation, Springer, New York, 1986.
  • [5] G. S. Fishman, Monte Carlo: Concepts, Algorithms and Applications, Springer, New York, 1996.
  • [6] L. Györfi and T. Nemetz, f-dissimilarity: A generalization of the affinity of several distributions, Ann. Inst. Statist. Math. 30 (1978), 105-113.
  • [7] G. Pólya and G. Szegő, Problems and Theorems in Analysis. Volume 1: Series, Integral Calculus, Theory of Functions, Springer, New York, 1972.
  • [8] A. L. Rukhin, Lower bound on the error probability for families with bounded likelihood ratios, Proc. Amer. Math. Soc. 119 (1993), 1307-1314.
  • [9] A. L. Rukhin, Recursive testing of multiple hypotheses: Consistency and efficiency of the Bayes rule, Ann. Statist. 22 (1994), 616-633.
  • [10] A. L. Rukhin, Change-point estimation: linear statistics and asymptotic Bayes risk, Math. Methods Statist. 5 (1996), 412-431.
  • [11] J. W. Tukey, Approximate weights, Ann. Math. Statist. 19 (1948), 91-92.
  • [12] I. Vajda, Theory of Statistical Inference and Information, Kluwer, Dordrecht, 1989.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-zmv24i4p415bwm
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