Abstract
A new approach to the definition of static relations between small amounts of input and output data is suggested, which is based on the use of randomized models and the estimation of probability characteristics of their parameters. To work up the procedures of robust parametric and nonparametric estimation, the entropy approach is developed, which uses generalized Boltzmann and Fermi informational entropies.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kendall, M.G. and Stuart, A., The Advanced Theory of Statistics, London: Charles Griffin, 1946, vol. 2. Translated under the title Statisticheskie vyvody i svyazi, Moscow: Nauka, 1973.
Cramer, G., Mathematical Methods of Statistics, Princeton: Princeton Univ. Press, 1946. Translated under the tirle Matematicheskie metody statistiki, Moscow: Mir, 1975.
Aivazyan, S.A. and Mkhitryan, V.S., Prikladnaya statistika i osnovy ekonometriki (Applied Statistics and Basis of Econometrics), Moscow: Interreklama, 2003.
Kobzar’, A.I., Prikladnaya matematicheskaya statistika (Applied Mathematical Statistics), Moscow: Fizmalit, 2006.
Golan, A., Judge, G., and Miller, D., Maximum Entropy Econometrics: Robust Estimation with Limited Data, New York: Wiley, 1996.
Golan, A., Information and Entropy Econometrics-A Review and Synthesis, Foundat. Trends Economet., 2006, vol. 2, nos. 1–2, pp. 1–145.
Shiryaev, A.N., Stokhasticheskaya finansovaya matematika (Stochastic FinancialMathematics), Moscow: Nauka, 2002.
Polyak, B.T. and Shcherbakov, P.S., Robastnaya ustoichivost’ i upravlenie (Robust Stability and Control), Moscow: Nauka, 2002.
Vapnik, V.N. and Chervonenkis, A.Ya., Teoriya raspoznavaniya obrazov (Pattern Recognition Theory), Moscow: Nauka, 1974.
Jaynes, E.T., Information Theory and Statistical Mechanics, Phys. Rev., 1957, vol. 106, pp. 620–630.
The Maximum Entropy Formalism, Levin, R.D. and Tribus M., Eds., Cambridge: MIT Press, 1979.
Jaynes, E.T., Papers on Probability, Statistics and Statistical Physics, Dordrecht: Kluwer, 1989.
Kapur, J.N., Maximum Entropy Models in Science and Engineering, New York: Wiley, 1989.
Jaynes, E.T., Probability Theory. The Logic and Science, Cambrige: Cambrige Univ. Press, 2003.
Racine, J. and Maasoumi, E., A Versatile and Robust Metric Entropy Test of Time-reversibility, and Other Hypotheses, J. Economet., 2007, vol. 138, pp. 547–567.
Huber, P.J., Robust Statistics, New York: Wiley, 1984.
Boltzmann, L., On the Link between the Second Beginning of Mechanical Calory Theory and Probability Theory in Theorems of Thermal Equilibrium, 1877. Translated in the series “Klassiki nauki” (Ckassics of Science), Moscow: Nauka, 1984, pp. 190–236.
Kullback, S. and Leibler, R.A., On Information and Sufficiency, Ann. Math. Statist., 1951, vol. 22(1), pp. 79–86.
Shannon, C., Communication Theory of Secrecy Systems, Bell Syst. Technic. J., 1949, vol. 28, no. 4, pp. 656–715.
Popkov, Yu.S., Teoriya makrosistem. Ravnovesnye modeli (Macrosystems Theory. Equilibrium Models), Moscow: URSS, 2012.
El’sgol’ts, L.Z., Variatsionnoe ischislenie (Calculus of Variations), Moscow: LKI, 2008.
Popkov, Yu.S., New Class of Multiplicative Algorithms for Solving Entropy-linear Programs, Eur. J. Oper. Res., 2006, vol. 174, pp. 1368–1379.
Author information
Authors and Affiliations
Additional information
Original Russian Text © Yu.S. Popkov, A.Yu. Popkov, Yu.N. Lysak, 2013, published in Avtomatika i Telemekhanika, 2013, No. 11, pp. 114–131.
Rights and permissions
About this article
Cite this article
Popkov, Y.S., Popkov, A.Y. & Lysak, Y.N. Estimation of characteristics of randomized static models of data (Entropy-robust approach). Autom Remote Control 74, 1863–1877 (2013). https://doi.org/10.1134/S0005117913110088
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117913110088