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Uspekhi Mat. Nauk, 1997, Volume 52, Issue 4(316), Pages 49–86 (Mi umn863)  

This article is cited in 21 scientific papers (total in 21 papers)

Dual extremal problems and their applications to minimax estimation problems

V. N. Solov'ev


DOI: https://doi.org/10.4213/rm863

Full text: PDF file (469 kB)
References: PDF file   HTML file

English version:
Russian Mathematical Surveys, 1997, 52:4, 685–720

Bibliographic databases:

UDC: 519.6+519.23
MSC: 46A20, 46A03
Received: 12.02.1996

Citation: V. N. Solov'ev, “Dual extremal problems and their applications to minimax estimation problems”, Uspekhi Mat. Nauk, 52:4(316) (1997), 49–86; Russian Math. Surveys, 52:4 (1997), 685–720

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. V. N. Solov'ev, “On the problem of minimax-Bayesian estimation”, Russian Math. Surveys, 53:5 (1998), 1104–1105  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    2. V. N. Solov'ev, “The subdifferential and the directional derivatives of the maximum of a family of convex functions”, Izv. Math., 62:4 (1998), 807–832  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. V. N. Soloviov, “Towards the Theory of Minimax-Bayesian Estimation”, Theory Probab Appl, 44:4 (2000), 739  mathnet  crossref  mathscinet  isi  elib
    4. Pankov, AR, “The parametric identification methods for many-dimensional linear models in the presence of a priori uncertainty”, Automation and Remote Control, 61:5 (2000), 785  mathnet  mathscinet  zmath  isi
    5. Soloviov V., “On the use of symmetry in optimal design of experiments”, Advances in Stochastic Simulation Methods, Statistics for Industry and Technology, 2000, 197–203  mathscinet  zmath  isi
    6. V. N. Solov'ev, “The subdifferential and the directional derivatives of the maximum of a family of convex functions. II”, Izv. Math., 65:1 (2001), 99–121  mathnet  crossref  crossref  mathscinet  zmath
    7. Pankov, AR, “Minimax quadratic optimization and its application to investment planning”, Automation and Remote Control, 62:12 (2001), 1978  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    8. Pankov, AR, “Minimax estimation in singular uncertain stochastic models”, Automation and Remote Control, 63:9 (2002), 1410  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
    9. Semenikhin, KV, “Minimax estimation of random elements by the root-mean-square criterion”, Journal of Computer and Systems Sciences International, 42:5 (2003), 670  mathscinet  zmath  isi  elib
    10. Bashkov, A, “Filtering problem for discrete Volterra equations with combined disturbances”, Stochastic Analysis and Applications, 25:6 (2007), 1297  crossref  mathscinet  zmath  isi  elib  scopus
    11. K. V. Semenikhin, “Minimax nature of the linear estimates of the indefinite stochastic vector from the generalized probabilistic criteria”, Autom. Remote Control, 68:11 (2007), 1970–1985  mathnet  crossref  mathscinet  zmath  elib  elib
    12. A. R. Pankov, K. V. Semenikhin, “Minimax estimation by probabilistic criterion”, Autom. Remote Control, 68:3 (2007), 430–445  mathnet  crossref  mathscinet  zmath  elib  elib
    13. Lebedev, MV, “Minimax filtering in a stochastic differential system with non-stationary perturbations of unknown intensity”, Journal of Computer and Systems Sciences International, 46:2 (2007), 206  crossref  mathscinet  zmath  isi  elib  scopus
    14. E. Yu. Ignashchenko, A. R. Pankov, K. V. Semenikhin, “Minimax-statistical approach to increasing reliability of measurement information processing”, Autom. Remote Control, 71:2 (2010), 241–256  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    15. Ignashchenko E.Yu., Pankov A.R., Semenikhin K.V., “A statistical minimax approach to optimizing linear models under a priori uncertainty conditions”, Journal of Computer and Systems Sciences International, 49:5 (2010), 710–718  crossref  mathscinet  zmath  isi  scopus  scopus
    16. Michel Volle, Jean-Baptiste Hiriart-Urruty, “A characterization of essentially strictly convex functions on reflexive Banach spaces”, Nonlinear Analysis: Theory, Methods & Applications, 2011  crossref  mathscinet  isi  scopus  scopus
    17. Medvedeva N.V., “Otsenivanie parametrov statisticheski neopredelennoi lineinoi modeli”, Vestnik Uralskogo gosudarstvennogo universiteta putei soobscheniya, 2011, no. 2, 4–12  elib
    18. A. A. Mamaev, K. V. Siemenikhin, “Minimax estimation methods under ellipsoidal constraints”, Autom. Remote Control, 74:4 (2013), 642–659  mathnet  crossref  isi
    19. E. N. Platonov, K. V. Semenikhin, “Methods for minimax estimation under elementwise covariance uncertainty”, Autom. Remote Control, 77:5 (2016), 817–838  mathnet  crossref  isi  elib  elib
    20. Myasnikov D.V. Siemenikhin K.V., “Control of M|M|1|N queue parameters under constraints”, J. Comput. Syst. Sci. Int., 55:1 (2016), 59–78  crossref  mathscinet  zmath  isi  elib  scopus
    21. A. S. Arkhipov, K. V. Semenikhin, “Minimax linear estimation with the probability criterion under unimodal noise and bounded parameters”, Autom. Remote Control, 81:7 (2020), 1176–1191  mathnet  crossref  crossref  isi  elib
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