THÈSE DE DOCTORAT DE L'UNIVERSITÉ PARIS 6 Spécialité ...

More documents

Recommendations

Info

Bibliographie 121BibliographieAdler, R. J. (1990). An introduction to continuity, extrema, and related topics for generalGaussian processes. Institute of Mathematical Statistics Lecture Notes—MonographSeries, 12. Institute of Mathematical Statistics, Hayward, CA.Akaike, H. (1973). Information theory and an extension of the maximum likelihood principle.In Second International Symposium on Information Theory (Tsahkadsor, 1971),pages 267–281. Akadémiai Kiadó, Budapest.Arestov, V. V. (1989). Optimal recovery of operators and related problems. Trudy Mat.Inst. Steklov., 189:3–20. Translated in Proc. Steklov Inst. Math. 1990, no. 4, 1–20, Acollection of papers from the All-Union School on the Theory of Functions (Russian)(Dushanbe, 1986).Baraud, Y. (2002). Model selection for regression on a random design. ESAIM Probab.Statist., 6:127–146 (electronic).Baraud, Y., Comte, F., and Viennet, G. (2001). Adaptive estimation in autoregression orβ-mixing regression via model selection. Ann. Statist., 29(3):839–875.Barron, A., Birgé, L., and Massart, P. (1999). Risk bounds for model selection via penalization.Probab. Theory Related Fields, 113(3):301–413.Belitser, E. N. and Levit, B. Y. (1995). On minimax filtering over ellipsoids. Math.Methods Statist., 4(3):259–273.Bertin, K. (2003). Asymptotically exact minimax estimation in sup-norm for anisotropicHölder classes. To appear in Bernoulli, Prépublication 811 du Laboratoire de Probabilitéset Modèles Aléatoires.Bertin, K. (2004). Minimax exact constant in sup-norm for nonparametric regression withrandom design. J. Statist. Plann. Inference, 123(2):225–242.Besov, O. V., Ilin, V. P., and Nikolskii, S. M. (1978). Integral representations of functionsand imbedding theorems. Vol. I. V. H. Winston & Sons, Washington, D.C. ScriptaSeries in Mathematics, Edited by Mitchell H. Taibleson.Brown, L. D., Cai, T. T., Low, M. G., and Zhang, C.-H. (2002). Asymptotic equivalencetheory for nonparametric regression with random design. Ann. Statist., 30(3):688–707.Dedicated to the memory of Lucien Le Cam.Brown, L. D. and Low, M. G. (1996). Asymptotic equivalence of nonparametric regressionand white noise. Ann. Statist., 24(6):2384–2398.
122 BibliographieButucea, C. (2001). Exact adaptive pointwise estimation on Sobolev classes of densities.ESAIM Probab. Statist., 5:1–31 (electronic).Butucea, C. and Neumann, M. (2004). Exact asymptotics for estimating the marginal densityof discretely observed diffusion processes. To appear in "bernoulli", Prépublicationdu laboratoire de Probabilités et Modèles Aléatoires.Catoni, O. (2001). Statistical learning theory and stochastic optimization. In Lectureson probability theory and statistics (Saint-Flour, 2001), Lecture Notes in Math., pages1–230. Springer, Berlin.Cavalier, L., Golubev, G. K., Picard, D., and Tsybakov, A. B. (2002). Oracle inequalitiesfor inverse problems. Ann. Statist., 30(3):843–874. Dedicated to the memory of LucienLe Cam.Cavalier, L. and Tsybakov, A. (2002). Sharp adaptation for inverse problems with randomnoise. Probab. Theory Related Fields, 123(3):323–354.Donoho, D. L. (1994a). Asymptotic minimax risk for sup-norm loss: solution via optimalrecovery. Probab. Theory Related Fields, 99(2):145–170.Donoho, D. L. (1994b). Statistical estimation and optimal recovery. Ann. Statist.,22(1):238–270.Donoho, D. L. and Johnstone, I. M. (1995). Adapting to unknown smoothness via waveletshrinkage. J. Amer. Statist. Assoc., 90(432):1200–1224.Donoho, D. L., Johnstone, I. M., Kerkyacharian, G., and Picard, D. (1995). Waveletshrinkage: asymptopia? J. Roy. Statist. Soc. Ser. B, 57(2):301–369. With discussionand a reply by the authors.Donoho, D. L. and Liu, R. C. (1991). Geometrizing rates of convergence. II, III. Ann.Statist., 19(2):633–667, 668–701.Donoho, D. L. and Low, M. G. (1992). Renormalization exponents and optimal pointwiserates of convergence. Ann. Statist., 20(2):944–970.Efroimovich, S. Y. and Pinsker, M. S. (1981). Estimation of square-integrable densityon the basis of a sequence of observations. Problems of Information Transmission,17:50–68.Efroimovich, S. Y. and Pinsker, M. S. (1982). Estimation of square-integrable probabilitydensity of a random variable. Problems of Information Transmission, 18:175–182.Efroimovich, S. Y. and Pinsker, M. S. (1984). A self-training algorithm for nonparametricfiltering. Automat. Remote Control, 11:1434–1440.Efromovich, S. (1996). On nonparametric regression for IID observations in a generalsetting. Ann. Statist., 24(3):1125–1144.Efromovich, S. (1999). Nonparametric curve estimation. Springer Series in Statistics.Springer-Verlag, New York. Methods, theory, and applications.Efromovich, S. (2000). On sharp adaptive estimation of multivariate curves. Math. MethodsStatist., 9(2):117–139.Farrell, R. H. (1967). On the lack of a uniformly consistent sequence of estimators of adensity function in certain cases. Ann. Math. Statist., 38:471–474.
Page 1:
THÈSE DE DOCTORAT DE L’UNIVERSIT
Page 4 and 5:
Table des matières 1Table des mati
Page 6 and 7:
Table des matières 3.2 Un théorè
Page 8 and 9:
1.1. Objet de la thèse 5blanc gaus
Page 10 and 11:
1.1. Objet de la thèse 7calculées
Page 12 and 13:
1.1. Objet de la thèse 9Un troisi
Page 14 and 15:
1.2. Principaux résultats 11où β
Page 16 and 17:
1.2. Principaux résultats 13le Cha
Page 18 and 19:
1.2. Principaux résultats 15où K
Page 20 and 21:
1.2. Principaux résultats 17de fon
Page 22 and 23:
1.2. Principaux résultats 19L > 0
Page 24 and 25:
Chapitre 2Asymptotically exact esti
Page 26 and 27:
2.2. The main result and the estima
Page 28 and 29:
2.2. The main result and the estima
Page 30 and 31:
2.3. Proofs 27We study the stochast
Page 32 and 33:
2.3. Proofs 29[for ε introduced in
Page 34 and 35:
2.3. Proofs 31where P θ,X is the d
Page 36 and 37:
2.3. Proofs 33as n → ∞ and usin
Page 38 and 39:
2.3. Proofs 35Thus some algebra and
Page 40 and 41:
2.3. Proofs 37Such choice of n is p
Page 42 and 43:
2.4. Appendix of Chapter 2 39• Fi
Page 44 and 45:
3.1. Introduction 41where ψ n = (
Page 46 and 47:
3.2. The estimator and main result
Page 48 and 49:
3.3. Upper bound 45Proof. The stoch
Page 50 and 51:
3.4. Lower bound 473.4 Lower boundB
Page 52 and 53:
3.4. Lower bound 49With these preli
Page 54 and 55:
3.5. Appendix of Chapter 3 51• If
Page 56 and 57:
3.5. Appendix of Chapter 3 53where
Page 58 and 59:
Chapitre 4Asymptotically exact mini
Page 60 and 61:
4.2. Main result 57with ˜β define
Page 62 and 63:
4.2. Main result 59(cf. Chapter 5 f
Page 64 and 65:
4.3. Upper bound 61Then we have( )
Page 66 and 67:
4.3. Upper bound 63where N Bj (u) i
Page 68 and 69:
4.4. Lower bound 65is a Gaussian ra
Page 70 and 71:
5.1. Cadre général de l’optimal
Page 72 and 73:
5.2. Application au problème d’a
Page 74 and 75: 5.2. Application au problème d’a
Page 84 and 85: 5.3. Lien entre l’optimal recover
Page 90 and 91: 5.4. Etudes des constantes 87sente
Page 92 and 93: 6.1. Introduction 89(where ‖g‖
Page 94 and 95: 6.2. Main results 91and we denote b
Page 96 and 97: 6.2. Main results 936.2.4 Exact asy
Page 98 and 99: 6.2. Main results 952. These result
Page 100 and 101: 6.3. Some preliminary results 97Pro
Page 102 and 103: 6.4. Proof of Theorem 6.1 99Let 0 <
Page 104 and 105: 6.4. Proof of Theorem 6.1 101where
Page 106 and 107: 6.5. Proof of Theorem 6.2 103withA
Page 108 and 109: 6.5. Proof of Theorem 6.2 105The qu
Page 110 and 111: 6.6. Proof of Theorem 6.3 107andwhe
Page 112 and 113: 6.6. Proof of Theorem 6.3 109By Pro
Page 114 and 115: 6.7. Proof of Theorem 6.4 111The pr
Page 116 and 117: 6.8. Proofs of the lemmas and propo
Page 122 and 123: 119Annexe.1 Résultats sur les proc
Page 126 and 127: Bibliographie 123Fuller, A. T. (196
Page 128 and 129: Bibliographie 125Micchelli, C. A. a
show all

THÈSE DE DOCTORAT DE L'UNIVERSITÉ PARIS 6 Spécialité ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?