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Bibliography
Barron A. Universal approximation bounds for superpositions of a sigmoidal function. IEEE Trans. on Information Theory, v. 39 No. 3 (1993).
Besov O.V., V.P. Il'in, and S.M. Nikol'ski. Integral representations of functions and embedding theorems, Moscow: Nauka Publishers, 1975) (in Russian)
Birgé L. Approximation dans les espaces métriques et théorie de l'estimation. Z. Wahrscheinlichkeitstheorie verw. Geb., v. 65 (1983), 181–237.
Cramer H. Mathematical Methods of Statistics, Princeton Univ. Press, Princeton, 1957.
Donoho D., I. Johnstone. Ideal spatial adaptation via wavelet shrinkage. Biometrika v. 81 (1994) No.3, 425–455.
Donoho D., I. Johnstone. Adapting to unknown smoothness via wavelet shrinkage. J. Amer. Statist. Assoc. v. 90 (1995) No. 432, 1200–1224.
Donoho D., I. Johnstone, G. Kerkyacharian, D. Picard. Wavelet shrinkage: Asymptopia? (with discussion and reply by the authors). J. Royal Statist. Soc. Series B v. 57 (1995) No.2, 301–369.
Eubank R. Spline smoothing and Nonparametric Regression, Dekker, New York, 1988.
Goldenshluger A., A. Nemirovski. On spatially adaptive estimation of nonparametric regression. Math. Methods of Statistics, v. 6 (1997) No. 2, 135–170.
Goldenshluger A., A. Nemirovski. Adaptive de-noising of signals satisfying differential inequalities. IEEE Transactions on Information Theory v. 43 (1997).
Golubev Yu. Asymptotic minimax estimation of regression function in additive model. Problemy peredachi informatsii, v. 28 (1992) No. 2, 3–15. (English transl. in Problems Inform. Transmission v. 28, 1992.)
Härdle W., Applied Nonparametric Regression, ES Monograph Series 19, Cambridge, U.K., Cambridge University Press, 1990.
Ibragimov I.A., R.Z. Khasminski. Statistical Estimation: Asymptotic Theory, Springer, 1981.
Ibragimov I., A. Nemirovski, R. Khas'minski. Some problems of nonparametric estimation in Gaussian white noise. Theory Probab. Appl. v. 31 (1986) No. 3, 391–406.
Juditsky, A. Wavelet estimators: Adapting to unknown smoothness. Math. Methods of Statistics v. 6 (1997) No. 1, 1–25.
Juditsky A., A. Nemirovski. Functional aggregation for nonparametric estimation. Technical report # 993 (March 1996), IRISA, Rennes
Korostelev A., A. Tsybakov. Minimax theory of image reconstruction. Lecture Notes in Statistics v. 82, Springer, New York, 1993.
Lepskii O. On a problem of adaptive estimation in Gaussian white noise. Theory of Probability and Its Applications, v. 35 (1990) No. 3, 454–466.
Lepskii O. Asymptotically minimax adaptive estimation I: Upper bounds. Optimally adaptive estimates. Theory of Probability and Its Applications, v. 36 (1991) No. 4, 682–697.
Lepskii O., E. Mammen, V. Spokoiny. Optimal spatial adaptation to inhomogeneous smoothness: an approach based on kernel estimates with variable bandwidth selectors. Ann. Statist. v. 25 (1997) No.3, 929–947.
Nemirovski A., D. Yudin. Problem complexity and method efficiency in Optimization, J. Wiley & Sons, 1983.
Nemirovski A. On forecast under uncertainty. Problemy peredachi informatsii, v. 17 (1981) No. 4, 73–83. (English transl. in Problems Inform. Transmission v. 17, 1981.)
Nemirovski A. On nonparametric estimation of smooth regression functions. Sov. J. Comput. Syst. Sci., v. 23 (1985) No. 6, 1–11.
Nemirovski A. On necessary conditions for efficient estimation of functionals of a nonparametric signal in white noise. Theory Probab. Appl. v. 35 (1990) No. 1, 94–103.
Nemirovski A. On nonparametric estimation of functions satisfying differential inequalities. — In: R. Khasminski, Ed. Advances in Soviet Mathematics, v. 12, American Mathematical Society, 1992, 7–43.
Pinsker M., Optimal filtration of square-integrable signals in Gaussian noise. Problemy peredachi informatsii, v. 16 (1980) No. 2, 120–133. (English transl. in Problems Inform. Transmission v. 16, 1980.)
Pinsker M., S. Efroimovich. Learning algorithm for nonparametric filtering. Automation and Remote Control, v. 45 (1984) No. 11, 1434–1440.
Pisier G. Remarques sur un resultat non publie de B. Maurey, — in: Seminaire d'analyse fonctionelle 1980–1981, v. 1–v. 12, Ecole Polytechnique, Palaiseau, 1981.
Prakasa Rao B.L.S. Nonparametric functional estimation. Academic Press, Orlando, 1983.
Rosenblatt M. Stochastic curve estimation. Institute of Mathematical Statistics, Hayward, California, 1991.
Suetin P.K. The classical orthogonal polynomials. Nauka, Moscow, 1976 (in Russian).
Wahba G. Spline models for observational data. SIAM, Philadelphia, 1990.
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Nemirovski, A. (2000). Estimating functionals, II. In: Bernard, P. (eds) Lectures on Probability Theory and Statistics. Lecture Notes in Mathematics, vol 1738. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0106718
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