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Volumn 28, Issue 2, 2000, Pages 500-531

Convergence rates of posterior distributions

Author keywords

Infinite dimensional model; Posterior distribution; Rate of convergence; Sieves; Splines

Indexed keywords


EID: 0034164796     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1016218228     Document Type: Article
Times cited : (643)

References (31)
  • 1
    • 0033438067 scopus 로고    scopus 로고
    • The consistency of posterior distributions in nonparametric problems
    • BARRON, A., SCHERVISH, M. J. and WASHERMAN, L. (1999). The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27 536-561.
    • (1999) Ann. Statist. , vol.27 , pp. 536-561
    • Barron, A.1    Schervish, M.J.2    Washerman, L.3
  • 2
    • 34250136988 scopus 로고
    • Approximation dans les espaces métriques et théorie de l'estimation
    • BIRGÉ, L. (1983). Approximation dans les espaces métriques et théorie de l'estimation. Z. Wahrsch. Verw. Gebiete 65 181-238.
    • (1983) Z. Wahrsch. Verw. Gebiete , vol.65 , pp. 181-238
    • Birgé, L.1
  • 3
    • 0002214856 scopus 로고
    • Sur un théorème de minimax et son application aux tests
    • BIRGÉ, L. (1984). Sur un théorème de minimax et son application aux tests. Probab. Math. Statist. 3 259-282.
    • (1984) Probab. Math. Statist. , vol.3 , pp. 259-282
    • Birgé, L.1
  • 4
    • 21344492381 scopus 로고
    • Rates of convergence for minimum contrast estimators
    • BIRGÉ, L. and MASSART, P. (1993). Rates of convergence for minimum contrast estimators. Probab. Theory Related Fields 97 113-150.
    • (1993) Probab. Theory Related Fields , vol.97 , pp. 113-150
    • Birgé, L.1    Massart, P.2
  • 5
    • 0003100694 scopus 로고    scopus 로고
    • From model selection to adaptive estimation
    • (G. Yang and D. Pollard, eds.). Springer, New York
    • BIRGÉ, L. and MASSART, P. (1997). From model selection to adaptive estimation. In Festschrift for Lucien Le Cam (G. Yang and D. Pollard, eds.) 55-87. Springer, New York.
    • (1997) Festschrift for Lucien Le Cam , pp. 55-87
    • Birgé, L.1    Massart, P.2
  • 6
    • 0000492892 scopus 로고    scopus 로고
    • Minimum contrast estimators on sieves: Exponential bounds and rates of convergence
    • BIRGÉ, L. and MASSART, P. (1998). Minimum contrast estimators on sieves: exponential bounds and rates of convergence. Bernoulli 4 329-375.
    • (1998) Bernoulli , vol.4 , pp. 329-375
    • Birgé, L.1    Massart, P.2
  • 8
    • 0003171807 scopus 로고
    • On the consistency of Bayes estimates
    • DIACONIS, P. and FREEDMAN, D. (1986). On the consistency of Bayes estimates (with discussion). Ann. Statist. 14 1-67.
    • (1986) Ann. Statist. , vol.14 , pp. 1-67
    • Diaconis, P.1    Freedman, D.2
  • 9
    • 0011083008 scopus 로고
    • Le calcul des probabilités et ses applications
    • DOOB, J. L. (1949). Le Calcul des Probabilités et ses Applications. Coll. Int. du CNRS 13 23-27.
    • (1949) Coll. Int. du CNRS , vol.13 , pp. 23-27
    • Doob, J.L.1
  • 10
    • 0000085854 scopus 로고
    • A course on empirical processes
    • Springer, Berlin
    • DUDLEY, R. M. (1984). A course on empirical processes. Lectures Notes in Math. 1097 2-141. Springer, Berlin.
    • (1984) Lectures Notes in Math. , vol.1097 , pp. 2-141
    • Dudley, R.M.1
  • 11
    • 0001120413 scopus 로고
    • A Bayesian analysis of some nonparametric problems
    • FERGUSON, T. S. (1973). A Bayesian analysis of some nonparametric problems. Ann. Statist. 1 209-230.
    • (1973) Ann. Statist. , vol.1 , pp. 209-230
    • Ferguson, T.S.1
  • 12
    • 0000780135 scopus 로고
    • Prior distribution on the spaces of probability measures
    • FERGUSON, T. S. (1974). Prior distribution on the spaces of probability measures. Ann. Statist. 2 615-629.
    • (1974) Ann. Statist. , vol.2 , pp. 615-629
    • Ferguson, T.S.1
  • 13
    • 0000202124 scopus 로고
    • On the asymptotic behavior of Bayes' estimates in the discrete case
    • FREEDMAN, D. A. (1963). On the asymptotic behavior of Bayes' estimates in the discrete case. Ann. Math. Statist. 34 1194-1216.
    • (1963) Ann. Math. Statist. , vol.34 , pp. 1194-1216
    • Freedman, D.A.1
  • 14
    • 0001446581 scopus 로고
    • On the asymptotic behavior of Bayes' estimates in the discrete case II
    • FREEDMAN, D. A. (1965). On the asymptotic behavior of Bayes' estimates in the discrete case II. Ann. Math. Statist. 36 454-456.
    • (1965) Ann. Math. Statist. , vol.36 , pp. 454-456
    • Freedman, D.A.1
  • 15
    • 0003226396 scopus 로고    scopus 로고
    • Non-informative priors via sieves and packing numbers
    • (S. Panchapakeshan and N. Balakrishnan eds.). Birkhäuser, Boston
    • GHOSAL, S., GHOSH, J. K. and RAMAMOORTHI, R. V. (1997). Non-informative priors via sieves and packing numbers. In Advances in Statistical Decision Theory and Applications (S. Panchapakeshan and N. Balakrishnan eds.) 129-140. Birkhäuser, Boston.
    • (1997) Advances in Statistical Decision Theory and Applications , pp. 129-140
    • Ghosal, S.1    Ghosh, J.K.2    Ramamoorthi, R.V.3
  • 16
    • 0033074585 scopus 로고    scopus 로고
    • Posterior consistency of Dirichlet mixtures in density estimation
    • GHOSAL, S., GHOSH, J. K. and RAMAMOORTHI R. V. (1999a). Posterior consistency of Dirichlet mixtures in density estimation. Ann. Statist. 27 143-158.
    • (1999) Ann. Statist. , vol.27 , pp. 143-158
    • Ghosal, S.1    Ghosh, J.K.2    Ramamoorthi, R.V.3
  • 19
    • 0000624821 scopus 로고
    • Epsilon-entropy and epsilon-capacity of sets in function spaces
    • KOLMOGOROV, A. N. and TIKHOMIROV, V. M. (1961). Epsilon-entropy and epsilon-capacity of sets in function spaces. Amer. Math. Soc. Trans. Ser. 2 17 277-364.
    • (1961) Amer. Math. Soc. Trans. Ser. 2 , vol.17 , pp. 277-364
    • Kolmogorov, A.N.1    Tikhomirov, V.M.2
  • 20
    • 0001786903 scopus 로고
    • Convergence of estimates under dimensionality restrictions
    • LE CAM, L. M. (1973). Convergence of estimates under dimensionality restrictions. Ann. Statist. 1 38-53.
    • (1973) Ann. Statist. , vol.1 , pp. 38-53
    • Le Cam, L.M.1
  • 26
    • 0001719983 scopus 로고
    • The dimensionality reduction principle for generalized additive models
    • STONE, C. J. (1986). The dimensionality reduction principle for generalized additive models. Ann. Statist. 14 590-606.
    • (1986) Ann. Statist. , vol.14 , pp. 590-606
    • Stone, C.J.1
  • 27
    • 0000645875 scopus 로고
    • Large-sample inference for log-spline models
    • STONE, C. J. (1990). Large-sample inference for log-spline models. Ann. Statist. 18 717-741.
    • (1990) Ann. Statist. , vol.18 , pp. 717-741
    • Stone, C.J.1
  • 28
    • 0346862811 scopus 로고
    • The use of polynomial splines and their tensor products in multivariate function estimation
    • STONE, C. J. (1994). The use of polynomial splines and their tensor products in multivariate function estimation (with discussion). Ann. Statist. 22 118-184.
    • (1994) Ann. Statist. , vol.22 , pp. 118-184
    • Stone, C.J.1
  • 31
    • 21844517288 scopus 로고
    • Probability inequalit es for likelihood ratios and convergence rates of sieve MLEs
    • WONG, W. H. and SHEN, X. (1995). Probability inequalit es for likelihood ratios and convergence rates of sieve MLEs. Ann. Statist. 23 339-362.
    • (1995) Ann. Statist. , vol.23 , pp. 339-362
    • Wong, W.H.1    Shen, X.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.