Vitesses de convergence de mesures a posteriori

Aad van der Vaart

Journal de la société française de statistique (2004)

  • Volume: 145, Issue: 1, page 7-30
  • ISSN: 1962-5197

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van der Vaart, Aad. "Vitesses de convergence de mesures a posteriori." Journal de la société française de statistique 145.1 (2004): 7-30. <http://eudml.org/doc/199287>.

@article{vanderVaart2004,
author = {van der Vaart, Aad},
journal = {Journal de la société française de statistique},
language = {fre},
number = {1},
pages = {7-30},
publisher = {Société française de statistique},
title = {Vitesses de convergence de mesures a posteriori},
url = {http://eudml.org/doc/199287},
volume = {145},
year = {2004},
}

TY - JOUR
AU - van der Vaart, Aad
TI - Vitesses de convergence de mesures a posteriori
JO - Journal de la société française de statistique
PY - 2004
PB - Société française de statistique
VL - 145
IS - 1
SP - 7
EP - 30
LA - fre
UR - http://eudml.org/doc/199287
ER -

References

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  1. [1] BIRGÉ L. ( 1983a). Approximation dans les espaces métriques et théorie de l'estimation. Z. Wahr. Verw. Gebiete 65, 181-238. Zbl0506.62026MR722129
  2. [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. Zbl0509.62036MR692785
  3. [3] DIACONIS P. and FREEDMAN D. (1986). On the consistency of Bayes estimates (with discussion). Ann. Statist. 14 1-67. Zbl0595.62022MR829555
  4. [4] ESCOBAR M. and WEST M. (1995). On Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90 577-588. Zbl0826.62021MR1340510
  5. [5] ESCOBAR M. (1994). Estimating normal means with a Dirichlet process prior. J. Amer. Statist. Assoc. 89 268-277. Zbl0791.62039MR1266299
  6. [6] FERGUSON T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. of Statistics 1 209-230. Zbl0255.62037MR350949
  7. [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. Zbl0557.62030MR736538
  8. [8] FREEDMAN D. (1963). On the asymptotic distribution of Bayes estimates in the discrete case I. Ann. Math. Statist. 34 1386-1403. Zbl0137.12603MR158483
  9. [9] GHOSAL S., GHOSH J. K. and VAN DER VAART, A. W. (2000). Convergence rates of posterior distributions. Ann. Statist. 28 500-531. Zbl1105.62315MR1790007
  10. [10] GHOSAL S., LEMBER J. and VAN DER VAART A. W. (2003). On Bayesian adaptation. Acta Applicandae Mathematica 79 165-175. Zbl1030.62030MR2021886
  11. [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. Zbl1043.62025MR1873329
  12. [12] GHOSAL S. and VAN DER VAART A. W. (2003). Posterior convergence rates of Dirichlet mixtures of normal for smooth densities. Preprint. Zbl1117.62046MR2003184
  13. [13] GHOSAL S. and VAN DER VAART A. W. (2003). Convergence rates for posterior distributions for noniid observations. Preprint. Zbl1114.62060MR2003184
  14. [14] GHOSH J. K. and RAMAMOORTHI R. V. (2003). Bayesian Nonparametrics. Springer-Verlag, New York. Zbl1029.62004MR1992245
  15. [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).) Zbl0090.33503MR112032
  16. [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. Zbl0052.15404MR54913
  17. [17] LE CAM L. M. (1973). Convergence of estimates under dimensionality restrictions. Ann. Statist. 22 38-53. Zbl0255.62006MR334381
  18. [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. Zbl0389.62011MR395005
  19. [19] LE CAM L. M. (1986). Asymptotic Methods in Statistical Decision Theory. Springer-Verlag, New York. Zbl0605.62002MR856411
  20. [20] LIU J.S. (2001). Monte Carlo Strategies in Scientific Computing. Springer-Verlag, New York. Zbl0991.65001MR1842342
  21. [21] ROBERT C.P. (2001). The Bayesian Choice : From Decision-Theoretic Foundations to Computational Implementation. Springer-Verlag, New York. Zbl0980.62005MR1835885
  22. [22] ROSENBLATT M. (1956). Remarks on some nonparametric estimates of a density function. Ann. Math. Statist. 27 832-837. Zbl0073.14602MR79873
  23. [23] SCHWARTZ L. (1965). On Bayes procedures. Z. Wahr. Verw. Gebiete 4 10-26. Zbl0158.17606MR184378
  24. [24] VAN DER VAART A. W. (1998). Asymptotic Statistics. Cambridge University Press. Zbl0910.62001MR1652247
  25. [25] VAN DER VAART A. W. and WELLNER J. A. (1996). Weak Convergence and Empirical Processes. Springer-Verlag, New York. Zbl0862.60002MR1385671
  26. [26] WEST M. (1992). Modeling with Mixtures. In Bayesian Statistics 4 (J.M. Bernardo et al, Eds.) 503-524. MR1380294

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