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Volumn 26, Issue 6, 1996, Pages 681-697

Uncertainty of discrete stochastic systems: General theory and statistical inference

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; DECISION MAKING; INFORMATION THEORY; PARAMETER ESTIMATION; STATISTICAL METHODS; STATISTICS; SYSTEMS ENGINEERING;

EID: 0030286376     PISSN: 10834427     EISSN: None     Source Type: Journal    
DOI: 10.1109/3468.541329     Document Type: Article
Times cited : (41)

References (70)
  • 2
    • 0000242156 scopus 로고
    • Information-theoretical considerations on estimation problems
    • S. Arimoto, "Information-theoretical considerations on estimation problems," Inform. Contr., vol. 19, pp. 181-194, 1971.
    • (1971) Inform. Contr. , vol.19 , pp. 181-194
    • Arimoto, S.1
  • 3
    • 0001388569 scopus 로고
    • On the statistical estimate of the entropy of a sequence of independent random variables
    • G. P. Basharin, "On the statistical estimate of the entropy of a sequence of independent random variables," Theory of Probability and Its Applications, vol. 4, pp. 361-364, 1959.
    • (1959) Theory of Probability and its Applications , vol.4 , pp. 361-364
    • Basharin, G.P.1
  • 4
    • 0018064415 scopus 로고
    • f-entropies, probability of error and feature selection
    • M. Ben Bassat, "f-entropies, probability of error and feature selection," Inform. Contr., vol. 39, pp. 227-242, 1978.
    • (1978) Inform. Contr. , vol.39 , pp. 227-242
    • Ben Bassat, M.1
  • 7
    • 1942502109 scopus 로고
    • Majorization, monotonicity of relative entropy and stochastic matrices
    • J. E. Cohen, Y. Derriennic, and Gh. Zbaganu, "Majorization, monotonicity of relative entropy and stochastic matrices," Contemp. Math., vol. 149, pp. 251-259, 1993.
    • (1993) Contemp. Math. , vol.149 , pp. 251-259
    • Cohen, J.E.1    Derriennic, Y.2    Zbaganu, Gh.3
  • 9
    • 84926662675 scopus 로고
    • Nearest neighbor pattern classification
    • T. M. Cover and P. E. Hart, "Nearest neighbor pattern classification," IEEE Trans. Inform. Theory, vol. 13, pp. 21-27, 1967.
    • (1967) IEEE Trans. Inform. Theory , vol.13 , pp. 21-27
    • Cover, T.M.1    Hart, P.E.2
  • 11
    • 0029219702 scopus 로고
    • Generalized cutoff rates and Renyi's information measures
    • I. Csiszár, "Generalized cutoff rates and Renyi's information measures," IEEE Trans. Inform. Theory, vol. 41, pp. 26-34, 1995.
    • (1995) IEEE Trans. Inform. Theory , vol.41 , pp. 26-34
    • Csiszár, I.1
  • 13
    • 0001317036 scopus 로고
    • Uncertainty, information and statistical experiments
    • M. H. De Groot, "Uncertainty, information and statistical experiments," Ann. Math. Statist., vol. 33, pp. 404-419, 1962.
    • (1962) Ann. Math. Statist. , vol.33 , pp. 404-419
    • De Groot, M.H.1
  • 16
    • 0001980960 scopus 로고
    • The distribution of general quadratic forms in normal variables
    • J. J. Dik and M. C. M. Gunst "The distribution of general quadratic forms in normal variables," Statistica Neerlandica, vol. 39, pp. 14-26, 1985.
    • (1985) Statistica Neerlandica , vol.39 , pp. 14-26
    • Dik, J.J.1    Gunst, M.C.M.2
  • 17
    • 0002434884 scopus 로고
    • Central Limit Theorem for nonstationary Markov chains I, II
    • R. L. Dobrushin, "Central Limit Theorem for nonstationary Markov chains I, II," Theory of Probability and Its Applications, vol. 1, pp. 65-80 and 329-383, 1956.
    • (1956) Theory of Probability and its Applications , vol.1 , pp. 65-80
    • Dobrushin, R.L.1
  • 20
    • 0038599379 scopus 로고
    • Zum Begriff der Entropie einer endlichen Wahrscheinlichkeitschemes
    • Berlin: Deutscher Verlag der Wissenschaften
    • D. K. Fadeev, "Zum Begriff der Entropie einer endlichen Wahrscheinlichkeitschemes," Arbeit zur Informationstheorie. Berlin: Deutscher Verlag der Wissenschaften, vol. 1, 1957.
    • (1957) Arbeit Zur Informationstheorie , vol.1
    • Fadeev, D.K.1
  • 21
    • 0027666905 scopus 로고    scopus 로고
    • Testing system entropy and prediction error probability
    • J. Feistauerová and I. Vajda, "Testing system entropy and prediction error probability," IEEE Trans. Syst., Man Cybern., vol. 23, pp. 1352-1358.
    • IEEE Trans. Syst., Man Cybern. , vol.23 , pp. 1352-1358
    • Feistauerová, J.1    Vajda, I.2
  • 22
    • 0040720585 scopus 로고    scopus 로고
    • Hypoentropy and related heterogenity divergence measures
    • C. Ferreri, "Hypoentropy and related heterogenity divergence measures," Statistica, vol. 40, pp. 55-118.
    • Statistica , vol.40 , pp. 55-118
    • Ferreri, C.1
  • 24
    • 0042003916 scopus 로고
    • Comparison of experiments and information measures
    • P. K. Goel and M. H. De Groot, "Comparison of experiments and information measures," Ann. Statist., vol. 7, pp. 1066-1077, 1979.
    • (1979) Ann. Statist. , vol.7 , pp. 1066-1077
    • Goel, P.K.1    De Groot, M.H.2
  • 26
    • 0000600466 scopus 로고
    • Some simple inequalities satisfied by convex functions
    • G. H. Hardy, J. E. Littlewood, and G. Pólya, "Some simple inequalities satisfied by convex functions," Messenger Math., vol. 58. pp. 145-152, 1929.
    • (1929) Messenger Math. , vol.58 , pp. 145-152
    • Hardy, G.H.1    Littlewood, J.E.2    Pólya, G.3
  • 27
    • 84980082105 scopus 로고
    • Transmission of information
    • R. V. L. Hartley, "Transmission of information," Bell Syst. Tech. J., vol. 7, pp. 535-545, 1928.
    • (1928) Bell Syst. Tech. J. , vol.7 , pp. 535-545
    • Hartley, R.V.L.1
  • 28
    • 0002453010 scopus 로고
    • The concept of structural a-entropy
    • J. Havrda and F. Charvát, "The concept of structural a-entropy," Kybernetika, vol. 3, pp. 30-35, 1967.
    • (1967) Kybernetika , vol.3 , pp. 30-35
    • Havrda, J.1    Charvát, F.2
  • 29
    • 0025209334 scopus 로고
    • Generalized entropy criteria for inverse problems, with applications to data compression, pattern classification and cluster analysis
    • L. K. Jones and C. L. Byrne, "Generalized entropy criteria for inverse problems, with applications to data compression, pattern classification and cluster analysis," IEEE Trans. Inform. Theory, vol. 36, pp. 23-30, 1990.
    • (1990) IEEE Trans. Inform. Theory , vol.36 , pp. 23-30
    • Jones, L.K.1    Byrne, C.L.2
  • 30
    • 0040302100 scopus 로고
    • Some new nonadditive measures of entropy
    • J. N. Kapur, "Some new nonadditive measures of entropy," Bull. U.M.I., pp. 253-266, 1988.
    • (1988) Bull. U.M.I. , pp. 253-266
    • Kapur, J.N.1
  • 31
    • 0022266928 scopus 로고
    • A new method for gray level picture thresholding using the entropy histogram
    • J. N. Kapur, P. K. Sahoo, and A. K. C. Wong, "A new method for gray level picture thresholding using the entropy histogram," Comput. Graphic, Vision, Image Processing, vol. 29, pp. 273-285, 1985.
    • (1985) Comput. Graphic, Vision, Image Processing , vol.29 , pp. 273-285
    • Kapur, J.N.1    Sahoo, P.K.2    Wong, A.K.C.3
  • 33
    • 0003007148 scopus 로고
    • The problem of character recognition from the point of view of mathematical statistics
    • V. A. Kovalevskij, Ed. New York: Spartan
    • V. A. Kovalevskij, "The problem of character recognition from the point of view of mathematical statistics," Character Readers and Pattern Recognition, V. A. Kovalevskij, Ed. New York: Spartan, 1968, pp. 3-30.
    • (1968) Character Readers and Pattern Recognition , pp. 3-30
    • Kovalevskij, V.A.1
  • 36
    • 84935761346 scopus 로고
    • Methods of measuring concentration of wealth
    • M. O. Lorenz, "Methods of measuring concentration of wealth," J. Amer. Statist. Assoc., vol. 9, pp. 209-219, 1905.
    • (1905) J. Amer. Statist. Assoc. , vol.9 , pp. 209-219
    • Lorenz, M.O.1
  • 38
    • 0000711292 scopus 로고
    • An index of diversity and the relation to certain concepts of diversity
    • R. P. McIntosh, "An index of diversity and the relation to certain concepts of diversity," Ecology, vol. 48, pp. 392 404, 1967.
    • (1967) Ecology , vol.48 , pp. 392404
    • McIntosh, R.P.1
  • 39
    • 38248998712 scopus 로고
    • A fuzzy probabilistic information system comparison criterion: Applications and properties
    • M. L. Menéndez, I. J. Taneja, and J. A. Pardo, "A fuzzy probabilistic information system comparison criterion: Applications and properties," Fuzzy Sets Syst., vol. 58, pp. 171-183, 1993.
    • (1993) Fuzzy Sets Syst. , vol.58 , pp. 171-183
    • Menéndez, M.L.1    Taneja, I.J.2    Pardo, J.A.3
  • 41
    • 4243824189 scopus 로고
    • Existence, uniqueness and evaluation of log-optimal investment portfolio
    • F. Österreicher and I. Vajda, "Existence, uniqueness and evaluation of log-optimal investment portfolio," Kybernetika, vol. 29, pp. 105-120, 1993.
    • (1993) Kybernetika , vol.29 , pp. 105-120
    • Österreicher, F.1    Vajda, I.2
  • 42
    • 0022896046 scopus 로고
    • Fuzzy set theoretic measure for automatic feature evaluation
    • S. K. Pal and B. Chakraborty, "Fuzzy set theoretic measure for automatic feature evaluation," IEEE Trans. Syst., Man, Cybern., vol. 16, pp. 754-760, 1986.
    • (1986) IEEE Trans. Syst., Man, Cybern. , vol.16 , pp. 754-760
    • Pal, S.K.1    Chakraborty, B.2
  • 43
    • 0026226855 scopus 로고
    • Entropy: A new definition and its applications
    • N. R. Pal and S. K. Pal, "Entropy: A new definition and its applications," IEEE Trans. Syst., Man, Cybern., vol. 21, pp. 1260-1270, 1991.
    • (1991) IEEE Trans. Syst., Man, Cybern. , vol.21 , pp. 1260-1270
    • Pal, N.R.1    Pal, S.K.2
  • 44
    • 38249008427 scopus 로고
    • Unified (r, s)-entropy as an index of diversity
    • L. Pardo, M. L. Menéndez, and J. A. Pardo, "Unified (r, s)-entropy as an index of diversity," J. Franklin Inst., vol. 329, pp. 907-921, 1992.
    • (1992) J. Franklin Inst. , vol.329 , pp. 907-921
    • Pardo, L.1    Menéndez, M.L.2    Pardo, J.A.3
  • 46
    • 0003143622 scopus 로고
    • Diversity and dissimilarity coefficients: A unified approach
    • C. R. Rao, "Diversity and dissimilarity coefficients: A unified approach," J. Theoret. Popul. Biol., vol. 21, pp. 24-43, 1982.
    • (1982) J. Theoret. Popul. Biol. , vol.21 , pp. 24-43
    • Rao, C.R.1
  • 49
    • 0003145851 scopus 로고
    • On the foundations of information theory
    • _, "On the foundations of information theory," Rev. Int. Statist. Inst., vol. 33, pp. 1-14, 1965.
    • (1965) Rev. Int. Statist. Inst. , vol.33 , pp. 1-14
  • 50
    • 0002983776 scopus 로고
    • Statistical aspects of neural networks
    • S. O. E. Barndorff-Nielsen, J. L. Jensen, and W. S. Kendall, Eds. London: Chapman and Hall
    • B. D. Ripley, "Statistical aspects of neural networks," Networks and Chaos, S. O. E. Barndorff-Nielsen, J. L. Jensen, and W. S. Kendall, Eds. London: Chapman and Hall, pp. 40-123, 1993.
    • (1993) Networks and Chaos , pp. 40-123
    • Ripley, B.D.1
  • 52
    • 0022059209 scopus 로고
    • Trigonometric entropies, Jensen difference divergences and error bounds
    • A. P. Sant'anna and I. J. Taneja, "Trigonometric entropies, Jensen difference divergences and error bounds," Inform. Sci., vol. 35, pp. 145-156, 1985.
    • (1985) Inform. Sci. , vol.35 , pp. 145-156
    • Sant'anna, A.P.1    Taneja, I.J.2
  • 53
    • 0002679616 scopus 로고
    • Über eine Klasse von Mittelbildungen mit Adwendungen die Determinanten-Theorie
    • I. Schur, "Über eine Klasse von Mittelbildungen mit Adwendungen die Determinanten-Theorie," Sitzungsber, Berlin Math. Gesellschaft, vol. 22, pp. 9-20, 1923.
    • (1923) Sitzungsber, Berlin Math. Gesellschaft , vol.22 , pp. 9-20
    • Schur, I.1
  • 54
    • 0040994282 scopus 로고
    • On the measurement of income inequality
    • R. R. Schutz, "On the measurement of income inequality," Amer. Econom. Rev., vol. 41, pp. 107-122, 1951.
    • (1951) Amer. Econom. Rev. , vol.41 , pp. 107-122
    • Schutz, R.R.1
  • 56
    • 84856043672 scopus 로고
    • A mathematical theory of communication
    • C. E. Shannon, "A mathematical theory of communication," Bell Syst. Tech. J., vol. 27, pp. 379-423 and 623-656, 1948.
    • (1948) Bell Syst. Tech. J. , vol.27 , pp. 379-423
    • Shannon, C.E.1
  • 57
    • 0001349617 scopus 로고
    • New nonadditive measures of relative information
    • B. D. Sharma and D. P. Mittal. "New nonadditive measures of relative information," J. Comb. Inform. Syst. Sci., vol. 2, pp. 122-133, 1975.
    • (1975) J. Comb. Inform. Syst. Sci. , vol.2 , pp. 122-133
    • Sharma, B.D.1    Mittal, D.P.2
  • 58
    • 0001072449 scopus 로고
    • Measurement of diversity
    • E. H. Simpson, "Measurement of diversity," Nature, vol. 163, p. 68, 1949.
    • (1949) Nature , vol.163 , pp. 68
    • Simpson, E.H.1
  • 60
    • 0006565340 scopus 로고
    • Uncertainty and the probability of error
    • D. L. Tebbe and S. J. Dwyer III, "Uncertainty and the probability of error," IEEE Trans. Inform. Theory, vol. 14, pp. 516-518, 1968.
    • (1968) IEEE Trans. Inform. Theory , vol.14 , pp. 516-518
    • Tebbe, D.L.1    Dwyer III, S.J.2
  • 61
    • 0006587258 scopus 로고
    • Bounds on the minimal error probability in checking a finite or countable number of hypotheses
    • I. Vajda, "Bounds on the minimal error probability in checking a finite or countable number of hypotheses," Inform. Transmission Problems, vol. 4, pp. 9-17, 1968.
    • (1968) Inform. Transmission Problems , vol.4 , pp. 9-17
    • Vajda, I.1
  • 62
    • 0001094901 scopus 로고
    • Axioms of a-entropy of a generalized probability scheme
    • _, "Axioms of a-entropy of a generalized probability scheme," Kybernetika, vol. 4, pp. 105-112, 1968.
    • (1968) Kybernetika , vol.4 , pp. 105-112
  • 63
    • 18244407921 scopus 로고
    • A contribution to informational analysis of patterns
    • S. Watanabe, Ed. New York: Academic
    • _, "A contribution to informational analysis of patterns," Methodologies of Pattern Recognition, S. Watanabe, Ed. New York: Academic, 1969.
    • (1969) Methodologies of Pattern Recognition
  • 64
    • 0021900007 scopus 로고
    • Majorization, concave entropies and comparison of experiments
    • I. Vajda and K. Vašek, "Majorization, concave entropies and comparison of experiments," Prob. Contr. Inform. Theory, vol. 14, pp. 105-115, 1985.
    • (1985) Prob. Contr. Inform. Theory , vol.14 , pp. 105-115
    • Vajda, I.1    Vašek, K.2
  • 66
    • 0027879269 scopus 로고
    • Measure of strife in Dempster-Schafer theory
    • J. Vejnarová and G. Klir, "Measure of strife in Dempster-Schafer theory," Int. J. General Syst., vol. 22, pp. 25-42, 1993.
    • (1993) Int. J. General Syst. , vol.22 , pp. 25-42
    • Vejnarová, J.1    Klir, G.2
  • 67
    • 33748085982 scopus 로고
    • M.Sc. Thesis, Faculty of Mathematics and Physics, Charles University, Prague, in Czech
    • P. Vosátka, "On some properties of conditional entropies," M.Sc. Thesis, Faculty of Mathematics and Physics, Charles University, Prague, 1969, in Czech.
    • (1969) On Some Properties of Conditional Entropies
    • Vosátka, P.1
  • 68
    • 0021491949 scopus 로고
    • Entropy and distance of random graphs with application to structural pattern recognition
    • A. K. C. Wong and M. You, "Entropy and distance of random graphs with application to structural pattern recognition," IEEE. Trans. Pattern Anal. Machine Intell., vol. 7, pp. 599-609, 1985.
    • (1985) IEEE. Trans. Pattern Anal. Machine Intell. , vol.7 , pp. 599-609
    • Wong, A.K.C.1    You, M.2
  • 70
    • 0005279278 scopus 로고
    • On measures of statistical dependence
    • J. Zvárová, "On measures of statistical dependence," Čas. Pêst. Matematiky, vol. 99, pp. 15-29, 1974.
    • (1974) Čas. Pêst. Matematiky , vol.99 , pp. 15-29
    • Zvárová, J.1


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