Generalization of discrimination-rate theorems of Chernoff and Stein
Kybernetika (1990)
- Volume: 26, Issue: 4, page 273-288
- ISSN: 0023-5954
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topVajda, Igor. "Generalization of discrimination-rate theorems of Chernoff and Stein." Kybernetika 26.4 (1990): 273-288. <http://eudml.org/doc/28590>.
@article{Vajda1990,
author = {Vajda, Igor},
journal = {Kybernetika},
keywords = {I-divergence; simple hypothesis; mixed errors; Bayes test; second kind errors; Neyman-Pearson tests; Rényi distances; inequalities; existence of an asymptotic Rényi distance; discrimination rates},
language = {eng},
number = {4},
pages = {273-288},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Generalization of discrimination-rate theorems of Chernoff and Stein},
url = {http://eudml.org/doc/28590},
volume = {26},
year = {1990},
}
TY - JOUR
AU - Vajda, Igor
TI - Generalization of discrimination-rate theorems of Chernoff and Stein
JO - Kybernetika
PY - 1990
PB - Institute of Information Theory and Automation AS CR
VL - 26
IS - 4
SP - 273
EP - 288
LA - eng
KW - I-divergence; simple hypothesis; mixed errors; Bayes test; second kind errors; Neyman-Pearson tests; Rényi distances; inequalities; existence of an asymptotic Rényi distance; discrimination rates
UR - http://eudml.org/doc/28590
ER -
References
top- P. H. Algoet, T.M. Cover, A sandwich proof of the Shannon-McMillan-Breiman theorem, Ann. Probab. 16 (1988), 899-909. (1988) Zbl0653.28013MR0929085
- A. Bhattacharyya, On some analogous to the amount of information and their uses in statistical estimation, Sankhya 8 (1946), 1-14. (1946) MR0020242
- H. Chernoff, A measure of asymptotic efficiency for tests of a hypothesis based on a sum of observations, Ann. Math. Statist. 23 (1952), 493-507. (1952) MR0057518
- H. Chernoff, Large sample theory: Parametric case, Ann. Math. Statist. 27 (1956), 1 - 22. (1956) Zbl0072.35703MR0076245
- R. S. Ellis, Large deviations for a general class of random vectors, Ann. Probab. 12 (1984), 1-12. (1984) Zbl0534.60026MR0723726
- R. S. Ellis, Entropy, Large Deviations, and Statistical Mechanics, Springer-Verlag. Berlin-Heidelberg-New York 1985. (1985) Zbl0566.60097
- I. I. Gikhman, A. V. Skorokhod, Stochastic Differential Equations (in Russian), Naukova Dumka, Kiev 1986. (1986)
- J. Hájek, A property of J-divergences or marginal probability distributions, Czechoslovak Math. J. 8 (1958), 460-463. (1958) MR0099712
- J. Hájek, On a property of normal distributions of an arbitrary stochastic process, Czechoslovak Math. J. 8 (1958), 610-618. (1958) MR0104290
- A. Janssen, Asymptotic properties of Neyman-Pearson test for infinite Kullback-Leibler information, Ann. Statist. 14 (1986), 1068-1079. (1986) MR0856806
- M. Janžura, Divergences of Gauss-Markov random fields with application to statistical inference, Kybernetika 24 (1988), 6, 401 - 412. (1988) MR0975850
- S. Kakutani, On equivalence of infinite product measures, Ann. of Math. 49 (1948), 214 - 226. (1948) Zbl0030.02303MR0023331
- E. I. Kolomietz, Asymptotic behaviour of type II errors of Neyman-Pearson test (in Russian), Teor. Veroyatnost. i Primenen. 33 (1986), 503 - 522. (1986)
- S. H. Koopmans, Asymptotic rate of discrimination for Markov processes, Ann. Math. Statist. 31 (1960), 982-994. (1960) Zbl0096.12603MR0119368
- O. Kraft, D. Plachky, Bounds for the power of likelihood ratio test and their asymptotic properties, Ann. Math. Statist. 41 (1970), 1646-1654. (1970) MR0272101
- S. Kullback J. C Keegel, and J. H. Kullback, Topics in Statistical Information Theory, Springer-Verlag, Berlin-Heidelberg-New York 1987. (1987) MR0904477
- H. Künsch, Thermodynamics and statistical analysis of Gaussian random fields, Z. Wahrsch. verw. Geb. 58 (1981) 407-421. (1981) MR0639149
- E. L. Lehman, Testing Statistical Hypotheses, J. Wiley, New York 1959. (1959) MR0852406
- F. Liese, Hellinger integrals of diffusion processes, Statistics 17 (1986), 63-78. (1986) Zbl0598.60042MR0827946
- F. Liese, I. Vajda, Convex Statistical Distances, Teubner, Leipzig 1987. (1987) Zbl0656.62004MR0926905
- J. Mémin, A. N. Shiryayev, Distances de Hellinger-Kakutani des lois correspondant á acroissements indépendants, Z. Wahrsch. verw. Geb. 70 (1985), 67-89. (1985) MR0795789
- T. Nemetz, On the -divergence rate for Markov-dependent hypotheses, Problems Control Inform. Theory 5(1974), 147-155. (1974) Zbl0303.62005MR0426254
- C M. Newman, The inner product of path space measures corresponding to random processes with independent increments, Bull. Amer. Math. Soc. 78 (1982), 268 - 272. (1982) MR0290453
- C M. Newman, The orthogonality of independent increment processes, In: Topics in Probability Theory (D. W. Strook, S. R. S. Varadhan, eds.), Convent Inst, of Math. Sciences, New York 1973, pp. 93-111. (1973) Zbl0269.60055MR0448532
- C M. Newman, B. W. Stuck, Chernoff bounds for discriminating between two Markov processes, Stochastics 2 (1979), 139-153. (1979) Zbl0408.62070MR0528906
- J. Oosterhooff, W. R. van Zwett, A note on contiguity and Hellinger distance, In: Contributions to Statistics (J. Hájek Memorial Volume, J. Jurečková, ed.), Reidel, Dordrecht 1979. (1979) MR0561267
- A. Perez, Notions generalises d'incertitude, d'entropie et d'information du point de vue de la theorie de martingales, In: Trans. 1st Prague Conf. on Inform. Theory, Statist. Dec. Functions, Random Processes. Publ. House Czechosl. Acad. Sci., Prague 1957, pp. 183 -206. (1957) MR0099889
- A. Perez, Generalization of ChernofTs result on the asymptote discernibility of two random processes, Colloq. Math. Soc. Janos Bolyai 9 (1974), 619 - 632. (1974) MR0388596
- M. S. Pinsker, Information and Information Stability of Random Variables and Processes, Holden-Day, San Francisco 1964. (1964) Zbl0125.09202MR0213190
- A. Rényi, On measures of entropy and information. In: Proc. 4th Berkeley Symp. on Probab, Theory Math. Statist., Vol. 1, Berkeley Univ. Press, Berkeley 1961, pp. 447-561. (1961) MR0132570
- I. Vajda, Limit theorems for total variation of cartesian product measures, Studia Sci. Math. Hungar. 6 (1971), 317-333. (1971) MR0310950
- I. Vajda, Theory of Statistical Inference and Information, Kluwer, Dordrecht-Boston 1989. (1989) Zbl0711.62002
- A. Wald, Statistical Decision Functions, J. Wiley, New York 1961. (1961) MR0036976
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