电邮这篇文章 
Approximate Estimation Using the Accelerated Maximum Entropy Method. Part 2. Study of the Properties of Estimates
- 作者: Dubnov Y.A.1, Boulytchev A.V.1
-
隶属关系:
- Federal Research Center “Computer Science and Control” of Russian Academy of Sciences
- 期: 编号 1 (2023)
- 页面: 71-81
- 栏目: Mathematical modeling
- URL: https://ogarev-online.ru/2071-8632/article/view/287844
- DOI: https://doi.org/10.14357/20718632230107
- ID: 287844
如何引用文章
开放存取
##reader.subscriptionAccessGranted##
订阅存取
详细
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.
作者简介
Y. Dubnov
Federal Research Center “Computer Science and Control” of Russian Academy of Sciences
编辑信件的主要联系方式.
Email: yury.dubnov@phystech.edu
Researcher, Senior Lecturer
俄罗斯联邦, MoscowA. Boulytchev
Federal Research Center “Computer Science and Control” of Russian Academy of Sciences
Email: bulytchev.isa.ran@gmail.com
PhD, Leading Researcher, Assistant Professor
俄罗斯联邦, Moscow参考
- Huang, David S. Regression and Econometric Methods. New York: John Wiley & Sons. 1970. pp. 127–147.
- Hazewinkel, Michiel, ed. "Bayesian approach to statistical problems", Encyclopedia of Mathematics, Springer. 2001.
- Amos Golan, George G. Judge, Douglas Miller. Maximum Entropy Econometrics: Robust Estimation with Limited Data. – John Wiley and Sons Ltd. Chichester, U.K., 1996.
- Kristofer Dougerti. Vvedenie v ekonometriku. — 2-e, per. s angl. — M.: INFRA-M, 2004. — 419 s.
- Ximing Wu. A Weighted Generalized Maximum Entropy Estimator with a Data-driven Weight // Entropy, 2009. no.11.
- 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.
- Lehmann, E. L.; Casella, G. (1998). Theory of Point Estimation (2nd ed.). Springer.
- Efron, B.; Tibshirani, R. (1993). An Introduction to the Bootstrap. Boca Raton, FL: Chapman & Hall/CRC.
- Popkov, Y.S.; Dubnov, Y.A.; Popkov, A.Y. New Method of Randomized Forecasting Using Entropy-Robust Estimation: Application to the World Population Prediction. // Mathematics, 2016, Vol. 4, Iss.1, p.1-16.
- Andrew Gelman. Bayes, Jeffreys, Prior Distributions and the Philosophy of Statistics // Statistical Science, vol.24, No.2, pp.176-178, 2009.
- Zellner A. Past and Recent Results on Maximal DataInformation Priors // Texhnical Report, Graduate School of Business, University of Chicago, 1996.
- Fink, Daniel (1997). "A Compendium of Conjugate Priors"
- R.D. Levin, M. Tribus. The maximum entropy formalism. MIT Press, 1979
- 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.
- Yu. S. Popkov. Soft Randomized Machine Learning // Doklady Mathematics, 2018, Vol. 98, No. 3, pp. 646–647.
- Fishman, George S. Monte Carlo : concepts, algorithms, and applications. — Springer, 1996.
- Rousseeuw, P. J., A. M. Leroy. Robust Regression and Outlier Detection. Wiley, 2003.
补充文件
