Vitesses de convergence de mesures a posteriori
Journal de la Société française de statistique, Volume 145 (2004) no. 1, pp. 7-30.
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van der Vaart, Aad. Vitesses de convergence de mesures a posteriori. Journal de la Société française de statistique, Volume 145 (2004) no. 1, pp. 7-30. http://www.numdam.org/item/JSFS_2004__145_1_7_0/

[1] Birgé L. ( 1983a). Approximation dans les espaces métriques et théorie de l'estimation. Z. Wahr. Verw. Gebiete 65, 181-238. | MR | Zbl

[2] Birgé L. ( 1983b). Robust testing for independent non-identically distributed variables and Markov chains. In Specifying Statistical Models. From Parametric to Non-Parametric. Using Bayesian or Non-Bayesian Approaches (J. P. Florens et al. eds.,) Lecture Notes in Statistics 16 Springer-Verlag, New York, 134-162. | MR | Zbl

[3] Diaconis P. and Freedman D. (1986). On the consistency of Bayes estimates (with discussion). Ann. Statist. 14 1-67. | MR | Zbl

[4] Escobar M. and West M. (1995). On Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90 577-588. | MR | Zbl

[5] Escobar M. (1994). Estimating normal means with a Dirichlet process prior. J. Amer. Statist. Assoc. 89 268-277. | MR | Zbl

[6] Ferguson T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. of Statistics 1 209-230. | MR | Zbl

[7] Ferguson T. S. (1983). Bayesian density estimation by mixtures of normal distributions. In Recent Advances in Statistics (Rizvi M., Rustagi, J. and Siegmund, D., Eds.) 287-302. | MR | Zbl

[8] Freedman D. (1963). On the asymptotic distribution of Bayes estimates in the discrete case I. Ann. Math. Statist. 34 1386-1403. | MR | Zbl

[9] Ghosal S., Ghosh J. K. and Van Der Vaart, A. W. (2000). Convergence rates of posterior distributions. Ann. Statist. 28 500-531. | MR | Zbl

[10] Ghosal S., Lember J. and Van Der Vaart A. W. (2003). On Bayesian adaptation. Acta Applicandae Mathematica 79 165-175. | MR | Zbl

[11] Ghosal S. and Van Der Vaart A. W. (2001). Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities. Ann. Statist. 29 1233-1263. | MR | Zbl

[12] Ghosal S. and Van Der Vaart A. W. (2003). Posterior convergence rates of Dirichlet mixtures of normal for smooth densities. Preprint. | MR

[13] Ghosal S. and Van Der Vaart A. W. (2003). Convergence rates for posterior distributions for noniid observations. Preprint. | MR

[14] Ghosh J. K. and Ramamoorthi R. V. (2003). Bayesian Nonparametrics. Springer-Verlag, New York. | MR | Zbl

[15] Kolmogorov A. N. and Tihomlrov V. M. (1961). ε-entropy and ε-capacity of sets in function spaces. Amer. Math. Soc. Transl. Ser. 2, 17 277-364. (Translated from Russian : Uspekhi Mat. Nauk 14 3-86, ( 1959).) | MR | Zbl

[16] Le Cam L. M. (1953). On some asymptotic properties of maximum likelihood estimates and related Bayes estimates. University of Califotnia Publications in Statistics 1 277-330. | MR | Zbl

[17] Le Cam L. M. (1973). Convergence of estimates under dimensionality restrictions. Ann. Statist. 22 38-53. | MR | Zbl

[18] Le Cam L. M. (1975). On local and global properties in the theory of asymptotic normality of experiments. In Stochastic Processes and Related Properties. Academic Press, New York, 13-54. | MR | Zbl

[19] Le Cam L. M. (1986). Asymptotic Methods in Statistical Decision Theory. Springer-Verlag, New York. | MR | Zbl

[20] Liu J.S. (2001). Monte Carlo Strategies in Scientific Computing. Springer-Verlag, New York. | MR | Zbl

[21] Robert C.P. (2001). The Bayesian Choice : From Decision-Theoretic Foundations to Computational Implementation. Springer-Verlag, New York. | MR | Zbl

[22] Rosenblatt M. (1956). Remarks on some nonparametric estimates of a density function. Ann. Math. Statist. 27 832-837. | MR | Zbl

[23] Schwartz L. (1965). On Bayes procedures. Z. Wahr. Verw. Gebiete 4 10-26. | MR | Zbl

[24] Van Der Vaart A. W. (1998). Asymptotic Statistics. Cambridge University Press. | MR | Zbl

[25] Van Der Vaart A. W. and Wellner J. A. (1996). Weak Convergence and Empirical Processes. Springer-Verlag, New York. | MR

[26] West M. (1992). Modeling with Mixtures. In Bayesian Statistics 4 (J.M. Bernardo et al, Eds.) 503-524. | MR