On Fano lemma and analogous inequalities for minimax risk. (Russian, English) Zbl 1051.62005

Gushchin, A. A.

Teor. Jmovirn. Mat. Stat. 67, 26-37 (2002); translation in Theory Probab. Math. Stat. 67, 29-42 (2003).

The author presents certain generalizations of the Fano lemma and Birgé inequalities [see L. Birgé, A new look at an old result: Fano’s lemma. Prépubl. N. 632, Laboratoire Probab. Modèles Aléatores, vol. 6 & 7, Univ. Paris (2001)] which provide a lower bound for minimax risks in the problem of distinguishing a finite number of simple hypotheses. In this framework, using an arbitrary \(f\)-divergence instead of the Kullback-Leibler information, the author derives a new inequality and demonstrated that all considered inequalities are exact.

Reviewer: N. M. Zinchenko (Kyïv)

MSC:

62B10	Statistical aspects of information-theoretic topics
62C20	Minimax procedures in statistical decision theory
62F03	Parametric hypothesis testing
62F15	Bayesian inference

Keywords:

Hypothesis testing; minimax risk; Kullback-Leibler information; Fano lemma