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Information-type divergence when the likelihood ratios are bounded

100%

Rukhin A. L.

Applicationes Mathematicae

1996-1997

tom 24

nr 4

415-423

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.

Estimating normal density and normal distribution function: is Kolmogorov's estimator admissible?

100%

Rukhin A. L.

Applicationes Mathematicae

1993-1995

tom 22

nr 1

103-115

The statistical estimation problem of the normal distribution function and of the density at a point is considered. The traditional unbiased estimators are shown to have Bayes nature and admissibility of related generalized Bayes procedures is proved. Also inadmissibility of the unbiased density estimator is demonstrated.

Ograniczanie wyników

2 Applicationes Mathematicae

2 Rukhin A. L.

1 1997

1 1993

Wyniki wyszukiwania

Information-type divergence when the likelihood ratios are bounded

Estimating normal density and normal distribution function: is Kolmogorov's estimator admissible?