DATA PROCESSING AND ANALYSIS
MATHEMATICAL MODELING
Yu. A. Dubnov, A. V. Boulytchev Approximate Estimation Using the Accelerated Maximum Entropy Method. Part 2. Study of the Properties of Estimates
INTELLIGENCE SYSTEMS AND TECHNOLOGIES
MANAGEMENT AND DECISION MAKING
MATHEMATICAL FOUNDATIONS OF INFORMATION TECHNOLOGY
Yu. A. Dubnov, A. V. Boulytchev Approximate Estimation Using the Accelerated Maximum Entropy Method. Part 2. Study of the Properties of Estimates
Abstract. 

In this paper, we investigate a method of approximate entropy estimation, designed to speed up the classical method of maximum entropy estimation due to the use of regularization in the optimization problem. This method is compared with the method of maximum likelihood and Bayesian estimation, both experimentally and in terms of theoretical calculations for some special cases. Estimation methods are tested on the example of a linear regression problem with errors of various types, including asymmetric distributions as well as a multimodal distribution in the form of a mixture of Gaussian components.

Keywords: 

probabilistic mathematical model, maximum entropy method, linear regression, regularization, errors distribution.

PP. 71-81.

DOI 10.14357/20718632230107
 
References

1. Huang, David S. Regression and Econometric Methods. New York: John Wiley & Sons. 1970. pp. 127–147.
2. Hazewinkel, Michiel, ed. "Bayesian approach to statistical problems", Encyclopedia of Mathematics, Springer. 2001.
3. Amos Golan, George G. Judge, Douglas Miller. Maximum Entropy Econometrics: Robust Estimation with Limited Data. – John Wiley and Sons Ltd. Chichester, U.K., 1996.
4. Kristofer Dougerti. Vvedenie v ekonometriku. — 2-e, per. s angl. — M.: INFRA-M, 2004. — 419 s.
5. Ximing Wu. A Weighted Generalized Maximum Entropy Estimator with a Data-driven Weight // Entropy, 2009. no.11.
6. Theil, Henri (1971). "Best Linear Unbiased Estimation and Prediction". Principles of Econometrics. New York: John Wiley & Sons. pp. 119–124. ISBN 0-471-85845-5.
7. Lehmann, E. L.; Casella, G. (1998). Theory of Point Estimation (2nd ed.). Springer.
8. Efron, B.; Tibshirani, R. (1993). An Introduction to the Bootstrap. Boca Raton, FL: Chapman & Hall/CRC.
9. Popkov, Y.S.; Dubnov, Y.A.; Popkov, A.Y. New Method of Randomized Forecasting Using Entropy-RobustEstimation: Application to the World Population Prediction. // Mathematics, 2016, Vol. 4, Iss.1, p.1-16.
10. Andrew Gelman. Bayes, Jeffreys, Prior Distributions and the Philosophy of Statistics // Statistical Science, vol.24, No.2, pp.176-178, 2009.
11. Zellner A. Past and Recent Results on Maximal DataInformation Priors // Texhnical Report, Graduate School of Business, University of Chicago, 1996.
12. Fink, Daniel (1997). "A Compendium of Conjugate Priors"
13. R.D. Levin, M. Tribus. The maximum entropy formalism. MIT Press, 1979
14. Yu. S. Popkov, Yu. A. Dubnov. Entropy-robust randomized forecasting under small sets of retrospective data // Automation and Remote Control. 2016, Volume 77, Issue 5, pp 839-854.
15. Yu. S. Popkov. Soft Randomized Machine Learning // Doklady Mathematics, 2018, Vol. 98, No. 3, pp. 646–647.
16. Fishman, George S. Monte Carlo : concepts, algorithms, and applications. — Springer, 1996.
17. Rousseeuw, P. J., A. M. Leroy. Robust Regression and Outlier Detection. Wiley, 2003.
 
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