Alexandre TSYBAKOV

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     Selected publications (1981-2000)

 

     Unpublished texts

     Books

Korostelev, A.P.,Tsybakov, A.B. (1993) Minimax Theory of Image Reconstruction. Lecture Notes in Statistics, v.82. Springer, NY e.a.

 

Härdle, W., Kerkyacharian, G., Picard, D.,Tsybakov, A.B. (1998) Wavelets, Approximation and Statistical Applications. Lecture Notes in Statistics, v.129, Springer, NY e.a.

 

Tsybakov, A.B. (2004) Introduction a l'estimation non-paramétrique. Springer.

 

     Selected publications

1. Error bounds for the method of minimization of empirical risk. Problems of Information Transmission, 17, n. 3, 33-42 (1981).
2. The method of minimization of the empirical risk in identification problems. Automation and Remote Control, n.9, 1196-1203 (1981).
3. Signal estimation when there is incomplete information on the noise distribution. Problems of Information Transmission, 18, n.2, 116-130 (1982).
4. Robust estimates of a function. Problems of Information Transmission, 18, n.3, 190-201 (1982).
5. On convergence of robust nonparametric algorithms of reconstruction of functions. Automation and Remote Control, v.44, n.12, part 1, 1582-1591 (1983).
6. Maximum likelihood method in nonparametric regression. Theory of Probability and its Applications, 28, n.4 (1983) [with Nemirovskii A.S., Polyak B.T.].
7. Estimators of maximum likelihood type for nonparametric regression. Soviet Mathematics Doklady, 28, n.3, 788-792 (1983) [with Nemirovskii A.S., Polyak B.T.].
8. Signal processing by the nonparametric maximum likelihood method. Problems of Information Transmission, 20, 177-192 (1984) [with Nemirovskii A.S., Polyak B.T.].
9. Rate of convergence of nonparametric estimators of maximum-likelihood type. Problems of Information Transmission, 21, 258-272 (1985) [with Nemirovskii A.S., Polyak B.T.].
10. Robust reconstruction of functions by the local-approximation method, Problems of Information Transmission, 22, 133-146 (1986).
11. Transmission accuracy of a continuous signal with binary quantization. Problems of Information Transmission, 23, n.1, 56-65 (1987).
12. On the choice of bandwidth in kernel nonparametric regression. Theory of Probability and its Applications, 32, 142-148 (1987).
13. Robust estimates of linear model parameters in a moving-average noise.Automation and Remote Control, v.48, n.6, part 2, 779-789 (1987) [with Onischenko V.F.].
14. Asymptotic normality of M-estimates. Automation and Remote Control, v.48, n.7, part 2, 926-936 (1987) [with Onischenko V.F.].
15. Robust nonparametric regression with simultaneous scale curve estimation. Annals of Statistics, 16, 120-135 (1988) [with Härdle W.].
16. Optimal projection estimators for a regression function with unknown smoothness. Soviet Mathematics Doklady, 39, n.1, 73-77 (1988) [with Polyak, B.T.].
17. Optimal estimation accuracy of nonsmooth images. Problems of Information Transmission, 25, n.3, 180-191 (1989).
18. Passive stochastic approximation. Automation and Remote Control, v.50, n.11, part 2, 1563-1569 (1989) [with Nazin, A.V., Polyak, B.T.]
19. Recursive estimation of the mode of a multivariate density. Problems of Information Transmission, 26, n.1, 31-37 (1990).
20. Locally-polynomial algorithms of passive stochastic approximation. Problems of Control and Information Theory, 19, n.3, 181-195 (1990).
21. Optimal rates of convergence for the global search stochastic optimization. Problems of Information Transmission, 26, n.2, 126-133 (1990) [with Polyak, B.T.].
22. Asymptotic optimality of Cp-criterion in projection-type regression estimation. Theory of Probability and its Applications, 35, n.2, 293-306 (1990) [with Polyak, B.T.].
23. Remarks on "Sliced inverse regression". Journal of the American Statistical Association, 86, n.414, 333-335 (1991) [with Härdle W.].
24. Optimal convergence rates of estimators in a statistical setup of the problem of tomography, Problems of Information Transmission, n.1, 73-81 (1991) [with Korostelev A.P.].
25. Nonparametric techniques in image estimation. In: Nonparametic Functional Estimation and Related Topics,
Procedings NATO ASI, Spetses (
Greece), July 29 - Aug.10, 1990, G.Roussas, ed., Kluwer, Dordrecht, 669-677 (1991).
26. Robust locally adaptive nonparametric regression. In: Data Analysis and Statistical Inference, Festschrift in honour of Friedhelm Eicker (Schach, S. and Trenkler, G., Ed.), Eul-Verlag,
Bergisch-Gladbach, 127-144 (1992) [with Härdle W.].
27. Bandwidth choice for average derivative estimation. Journal of the American Statistical Association,
87,n.417, 218-226 (1992) [with Härdle W., Hart, J., Marron J.S.].
28. Asymptotically minimax image reconstruction problems. In Topics in Nonparametric Estimation, Khasminskii R.Z., ed., American Mathematical Society, Providence, R.I., 45-86 (1992) [with Korostelev A.P.].
29. Optimal and robust algorithms of passive stochastic approximation. IEEE Transactions on Information Theory, v.38, n.5, 1577-1583 (1992) [with Nazin, A.V., Polyak, B.T.]
30. On stochastic approximation with arbitrarily dependent noise. In Topics in Nonparametric Estimation, Khasminskii R.Z., ed., American Mathematical Society, Providence, R.I., 107-113 (1992) [with Polyak, B.T.].
31. The family of asymptotically optimal methods of the choice of the order in orthogonal series regression estimation. Theory of Probability and its Applications, v.37, n.3, 501-511 (1992) [with Polyak, B.T.].
32. Estimation of the density support and its functionals. Problems of Information Transmission, v.29, n.1, 1-15 (1993) [with Korostelev A.P.].
33. Minimax linewise algorithm for image reconstruction. In Computer Intensive Methods in Statistics (Härdle W. and Simar L. eds) Physica-Verlag, Berlin, 113-133 (1993) [with Korostelev A.P.].
34. How sensitive are average derivatives? Journal of Econometrics, v.58, 31-48 (1993) [with Härdle W.].
35. Robust recursive estimation in non-linear ARX-models. Problems of Information Transmission, v.29, n.4, 318-327 (1993) [with Doukhan, P.].
36. On efficient estimation of average derivative. Doklady of Russian Academy of Sciences, v.331, n.5, 550-552 (1993) [with Ibragimov, I.A., Härdle, W.].
37. Asymptotic efficiency in estimation of a convex set. Problems of Information Transmission,
v.30, n.4, 317-327 (1994) [with Korostelev A.P.].
38. Multidimensional change-point problems and boundary estimation. In: Change-Point Problems (E.Carlstein, H.G.Muller, and D.Siegmund eds.), IMS Lecture Notes Monograph Series, vol.23, Hayward, California, p.317-329 (1994).
39. Asymptotical minimax recovery of sets with smooth boundaries. Annals of Statistics, v.23, n.2, 502-524 (1995)
[with Mammen E.].
40. Efficient estimation of monotone boundaries. Annals of Statistics, v.23, n.2, p.476-489 (1995) [with Korostelev A.P., Simar L.].
41. Visual error criteria for qualitative smoothing. Journal of the American Statistical Association,
v.90, n.430, 499-507 (1995) [with Marron J.S.].
42. On estimation of monotone and convex boundaries. Publications de l'Institut de Statistique de l'Universite de Paris, v.39, 3-18 (1995) [with Korostelev A.P., Simar L.].
43. Additive nonparametric regression on principal components. Journal of Nonparametric Statistics, v.5, 157-184 (1995) [with Härdle W.].
44. Discussion on "Wavelet Shrinkage: Asymptopia?". Journal of the Royal Statistical Society B, v.57, n.1. p.360 (1995).
45. Nonparametric recursive variance estimation. Statistics, v.27, 55-63 (1995) [with
Stadtmuller U.].
46. Estimation of non-sharp support boundaries. Journal of Multivariate Analysis, v.55, n.2, 205-218 (1995) [with Härdle W., Park B.U.].
47. Root-n consistent estimators of entropy for densities with unbounded support. Scandinavian Journal of Statistics, v.23, 75-83 (1996) [with van der Meulen E.C.].
48. Asymptotically efficient estimation of analytic functions in Gaussian noise.  Bernoulli, v.2, 167-181 (1996) [with Golubev,Y.K., Levit,B.Y.].
49. Local polynomial estimators of the volatility function in nonparametric autoregression. Journal of Econometrics, v.81, 223-242 (1997) [with Härdle W.].
50. Asymptotically efficient signal estimation in L2 under general loss functions. Problems of Information Transmission, v.33, n.1, 78-88 (1997).
51. On nonparametric estimation of density level sets. Annals of Statistics, v.25, 948-969 (1997).
52. Exact asymptotic minimax constants for the estimation of analytical functions in Lp. Probability Theory and
Related Fields
, v.112, 33-51 (1998) [with Guerre, E.].
53. Nonparametric vector autoregression. Journal of Statistical Planning and Inference,
v.68, 221-245 (1998) [with H\"ardle W., Yang L.J.].
54. Pointwise and sup-norm sharp adaptive estimation of functions on the Sobolev classes. Annals of Statistics, 26, 2420-2469 (1998).
55. Smooth discrimination analysis. Annals of Statistics, 27, 1808 - 1829 (1999) [with Mammen, E.].
56. On the best rate of adaptive estimation in some inverse problems. C.R. Acad. Sci. Paris, ser. 1, t.330, 835-840 (2000).
57. Asymptotically exact nonparametric hypothesis testing in sup-norm and at a fixed point. Probability Theory and Related Fields, 117, 17-48 (2000) [with Lepski O.V.].
58. Thresholding algorithms, maxisets and well-concentrated bases: a discussion. Test, 9, 338-340 (2000).

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     Unpublished texts

Root-n consistent estimators of entropy for densities with unbounded support. Discussion paper n.9206, Institut de Statistique, Université Catholique de Louvain (1992) [with van der Meulen E.C.] Partly published in Scandinavian Journal of Statistics, v.23, 75-83 (1996)

Adaptive estimation for inverse problems: a logarithmic effect in L_2. Prépublication du LPMA n. 579 (2000). Short version published in C.R. Acad. Sci. Paris, ser. 1, t.330, 835-840 (2000).

Aggregation for regression learning. Prépublication du LPMA n. 948 (2004) [with Bunea F., Wegkamp M.], arXiv:math.ST/0410214, 8 Oct. 2004.

 

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