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Stochastic recovery problem

  • Methods of Signal Processing
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Abstract

We consider the problem of estimating a functional defined on some functional class from observations (with noise) of values of other functionals at the same functional class. In general, all functionals are nonlinear. We propose a formal mathematical statement of the problem. For the proposed statement, we give a nonasymptotically optimal estimation method under rather weak constraints on the estimated functional and noise. Some examples are considered.

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References

  1. Micchelli, C.A. and Rivlin, T.J., Lectures on Optimal Recovery, Lect. Notes Math., Berlin: Springer, 1985, vol. 1129, pp. 21–93.

    Google Scholar 

  2. Magaril-Il’yaev, G.G., Osipenko, K.Yu., and Tikhomirov, V.M., Indefinite Knowledge about an Object and Accuracy of Its Recovery Methods, Probl. Peredachi Inf., 2003, vol. 39, no. 1, pp. 118–133 [Probl. Inf. Trans. (Engl. Transl.), 2003, vol. 39, no. 1, pp. 104–118].

    MathSciNet  Google Scholar 

  3. Magaril-Il’yaev, G.G. and Tikhomirov, V.M., Vypuklyi analiz i ego prilozheniya, Moscow: Editorial URSS, 2000. Translated under the title Convex Analysis: Theory and Applications, Providence: Amer. Math. Soc., 2003.

    Google Scholar 

  4. Traub, J.F. and Woźniakowski, H., A General Theory of Optimal Algorithms, New York: Academic, 1980.

    MATH  Google Scholar 

  5. Darkhovskii, B.S., On a Stochastic Recovery Problem, Teor. Veroyatnost. i Primenen., 1998, vol. 43, no. 2, pp. 357–364 [Theory Probab. Appl. (Engl. Transl.), 1999, vol. 43, no. 2, pp. 282–288].

    MathSciNet  Google Scholar 

  6. Darkhovskii, B.S., A New Approach to a Stochastic Renewal Problem, Teor. Veroyatnost. i Primenen., 2004, vol. 49, no. 1, pp. 36–53 [Theory Probab. Appl. (Engl. Transl.), 2005, vol. 49, no. 1, pp. 51–64].

    MathSciNet  Google Scholar 

  7. Magaril-Il’yaev, G.G., Osipenko, K.Yu., and Tikhomirov, V.M., Optimal Reconstruction and Extremum Theory, Dokl. Ross. Akad. Nauk, 2001, vol. 379, no. 2, pp. 161–164 [Dokl. Math. (Engl. Transl.), 2001, vol. 64, no. 1, pp. 32–35].

    MathSciNet  Google Scholar 

  8. Ioffe, A.D. and Tikhomirov, V.M., Teoriya ekstremal’nykh zadach, Moscow: Nauka, 1974. Translated under the title Theory of Extremal Problems, Amsterdam: North-Holland, 1979.

    Google Scholar 

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Authors and Affiliations

  1. Institute for Systems Analysis, RAS, Moscow, Russia

    B. S. Darkhovsky

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  1. B. S. Darkhovsky
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Correspondence to B. S. Darkhovsky.

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Original Russian Text © B.S. Darkhovsky, 2008, published in Problemy Peredachi Informatsii, 2008, Vol. 44, No. 4, pp. 20–32.

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Darkhovsky, B.S. Stochastic recovery problem. Probl Inf Transm 44, 303–314 (2008). https://doi.org/10.1134/S0032946008040030

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  • DOI: https://doi.org/10.1134/S0032946008040030

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