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International Theoretical Science Journal
Volume 59 >>> № 6 NOVEMBER — DECEMBER 2023
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UDC 519.21
M.S. Dunaievskyi1


1 V.M. Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, Kyiv, Ukraine

 MaxDunaievskyi@gmail.com

M-ESTIMATES: A REVIEW AND APPLICATION FOR DECISION-MAKING
UNDER UNCERTAINTY

Abstract. A brief overview of the evolution of the robust estimate methods is presented, in particular, the main concepts of m-estimation methods and their advantages when working with data containing statistical outliers. The comparison of the results of the methods of M-estimates by P. Huber, F. Hampel, and the method of biquadratic weights by J. Tukey was held on real economic data of the regions of Ukraine. We have got empirical confirmation of the efficiency of using M-estimates. The comparison of all the generated models indicates a significant shift in parameter estimates, in case, the approach of naive removal of statistical outliers has been applied. Based on the constructed robust models, we can more accurately compare the regions of the country in terms of the labor and capital factors efficiency, and accordingly determine the priority of investments that will stimulate the economic development of the region to a greater extent.

Keywords: decentralization, decision-making, M-estimates, regional development, robustness, uncertainty.


full text

REFERENCES

  1. Huber P.J. Robust statistics. New York: John Wiley & Sons, 1981. 317 p.

  2. Hampel F.R., Ronchetti E.M., Rousseeuw P.J., Stahel W.A. Robust statistics: The approach based on influence functions. New York: John Wiley & Sons, 1986. 536 p.

  3. Marazzi A. Algorithms, routines and S functions for robust statistics. Wadsworth & Brooks/Cole, 1993. 440 p.

  4. De Moivre A. The doctrine of chances: or, A method for calculating the probabilities of events in play. 3rd ed. London: A. Millar, 1756. 348 p.

  5. Green Jr. B.F., Tukey J.W. Complex analyses of variance: General problems. Psychometrika. 1960. Vol. 25, Iss. 2. P. 127–152. https://doi.org/10.1007/BF02288577 .

  6. Tukey J.W. The future of data analysis. The Annals of Mathematical Statistics. 1962. Vol. 33, N 1. P. 1–67. http://www.jstor.org/stable/2237638.

  7. Huber P.J. Robust estimation of a location parameter. The Annals of Mathematical Statistics. 1964. Vol. 35, N 1. P. 73–101. https://doi.org/10.1214/aoms/1177703732.

  8. Hampel F.R. Contributions to the theory of robust estimation: PhD thesis. University of California, 1968. 206 p.

  9. Box G.E.P. Non-normality and tests on variances. Biometrika. 1953. Vol. 40, Iss. 3–4. P. 318–335. https://doi.org/10.2307/2333350 .

  10. Huber P.J., Ronchetti E.M. Robust statistics. Wiley & Sons, Inc., 2009. 384 p. https://doi.org/10.1002/9780470434697.

  11. Beaton A.E., Tukey J.W. The fitting of power series, meaning polynomials, illustrated on band-spectroscopic data. Technometrics. 1974. Vol. 16, Iss. 2. P. 147–185.

  12. Andrews D.F., Bickel P.J., Hampel F.R., Huber P.J., Rogers W.H., Tukey J.W. Robust estimates of location: Survey and advances. Princeton, NJ: Princeton University Press, 1972. 374 p.

  13. Gorbachuk V.M., Ermoliev Yu.M., Ermolieva T.Yu., Dunaevskyi M.S. Application of quantile regression for assessment of environmental and economic risks. V International Scientific and Practical Conference "Computational Intelligence" (April 15–20, 2019, Uzhhorod, Ukraine). Uzhgorod, 2019. P. 188–189.

  14. Ermoliev Yu.M., Knopov P.S. Method of empirical means in stochastic programming problems. Cybernetics and Systems Analysis. 2006. Vol. 42, N 6. P. 773–785. https://doi.org/10.1007/s10559-006-0118-z .

  15. Dorogovtsev A.Ya. Theory of parameter estimates for random processes [in Russian]. Kyiv: Vishcha shkola., 1982. 192 с.

  16. Korkhin A.S. On some properties of regression parameter estimates under a priori inequality constraints. Kibernetika. 1985. N 6. P. 106–114.

  17. Knopov P.S. Asymptotic properties of some classes of M-estimates. Cybernetics and Systems Analysis. 1997. Vol. 33, N. 4. P. 468–481. https://doi.org/10.1007/BF02733103.

  18. Mikhalevich V.S., Knopov P.S., Golodnikov A.N. Mathematical models and methods of risk assessment in ecologically hazardous industries. Cybernetics and Systems Analysis. 1994. Vol. 30, N 2. P. 259–273. https://doi.org/10.1007/BF02366429 .

  19. Knopov P.S., Kasitskaya E.J. Empirical estimates in stochastic optimization and identification. NY: Springer New York, 2002. VIII, 250 p. https://doi.org/10.1007/978-1-4757-3567-3

  20. Knopov P.S., Norkin V.I. Stochastic optimization of the stochastic storage processes. Proc. International Conference «Modern Stochastics: Theory and Applications V» (MSTA-V) (1–4 June 2021, Kyiv, Ukraine). Kyiv, 2021. P. 68–69.

  21. Dunaevskyi M.S. Empirical averages in stochastic programming problems. Proceedings of the symposium "Intellectual solutions", school-seminar "Theory of decision-making" (September 28–30, 2021, Uzhhorod, Ukraine). Uzhgorod, 2021. P. 111–112. URL: https://intsol.knu.ua/conference-proceedings/.

  22. Gorbachuk V.M., Dunaevskyi M.S., Suleymanov S.-B. The growth model of a decentralized economy with Cobb–Douglas production functions. Eastern Europe: Economy, Business and Management.2019. Iss. 6 (23). P. 738–746.

  23. Gorbachuk V.M., Makarenko O.S., Dunaevskyi M.S., Novoderezhkin V.I., Suleymanov S.-B. Measuring the economic efficiency of the regions of Ukraine for the first quarters of 2017. Proceedings of the conference "Modern informatics: problems, achievements and development prospects" (December 13–15, 2017, Kyiv, Ukraine). Kyiv, 2017. P. 258–260.

  24. Dunaevskyi M.S. Economic growth of adjacent districts under decentralization. Teoriya optymalʹnykh rishen'. 2019. N 18. P. 94–99.

  25. Gorbachuk V., Dunaievskyi M., Suleimanov S.-B. Modeling of agency problems in complex decentralized systems under information asymmetry. Proc. 2019 IEEE International Conference on Advanced Trends in Information Theory (ATIT) (18–19 December 2019, Kyiv, Ukraine). Kyiv, 2019. P. 449–454. https://doi.org/10.1109/ATIT49449.2019.9030498.

  26. State Statistics Service of Ukraine. Statistical bulletin "Socio-economic situation of the region" (for each region separately). URL: https://ukrstat.gov.ua/druk/ publicat/kat_u/2017/soc_ek_reg/publ_arch_reg_u.htm (дата звернення: 01.09.2023) .

  27. On the creation and liquidation of districts: Resolution of the Verkhovna Rada of July 17, 2020 No. 807-IX: as of September 1, 2023. URL: https://zakon.rada.gov.ua/laws/show/807-20#Text (application date: 01.09.2023).




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