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Volumn 29, Issue 5, 2001, Pages 1233-1263

Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities

Author keywords

Bracketing; Dirichlet mixture; Entropy; Maximum likelihood; Mixture of normals; Posterior distribution; Rate of convergence; Sieve

Indexed keywords


EID: 0035470893     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/aos/1013203452     Document Type: Article
Times cited : (218)

References (34)
  • 1
    • 0027453616 scopus 로고
    • Model based Gaussian and non-Gaussian clustering
    • BANFIELD, J. and RAFTERY, A. (1993). Model based Gaussian and non-Gaussian clustering. Biometrics 49 803-821.
    • (1993) Biometrics , vol.49 , pp. 803-821
    • Banfield, J.1    Raftery, A.2
  • 2
    • 0033438067 scopus 로고    scopus 로고
    • The consistency of posterior distributions in nonparametric problems
    • BARKON, A., SCHERVISH, M. and WASSERMAN, L. (1999). The consistency of posterior distributions in nonparametric problems. Ann. Statist. 27 536-561.
    • (1999) Ann. Statist. , vol.27 , pp. 536-561
    • Barkon, A.1    Schervish, M.2    Wasserman, L.3
  • 3
    • 0000492892 scopus 로고    scopus 로고
    • Minimum contract estimators on sieves: Exponential bounds and rates of convergence
    • BIRGÉ, L. and MASSART, P. (1998). Minimum contract 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
  • 4
    • 84950937290 scopus 로고
    • Bayesian density estimation and inference using mixtures
    • ESCOBAR, M. and WEST, M. (1995). Bayesian density estimation and inference using mixtures. J. Amer. Statist. Assoc. 90 577-588.
    • (1995) J. Amer. Statist. Assoc. , vol.90 , pp. 577-588
    • Escobar, M.1    West, M.2
  • 6
    • 0001787029 scopus 로고
    • Bayesian density estimation by mixtures of normal distributions
    • M. Rizvi, J. Rustagi and D. Siegmund, eds. Academic Press, New York
    • FERGUSON, T. S. (1983). Bayesian density estimation by mixtures of Normal distributions. In Recent Advances in Statistics (M. Rizvi, J. Rustagi and D. Siegmund, eds.) 287-302. Academic Press, New York.
    • (1983) Recent Advances in Statistics , pp. 287-302
    • Ferguson, T.S.1
  • 7
    • 0001414599 scopus 로고
    • Nonparametric maximum likelihood estimation by the method of sieves
    • GEMAN, S. and HWANG, C. (1982). Nonparametric maximum likelihood estimation by the method of sieves. Ann. Statist. 10 401-414.
    • (1982) Ann. Statist. , vol.10 , pp. 401-414
    • Geman, S.1    Hwang, C.2
  • 8
    • 0034237946 scopus 로고    scopus 로고
    • Rates of convergence for the Gaussian mixture sieve
    • GENOVESE, C. and WASSERMAN, L. (2000). Rates of convergence for the Gaussian mixture sieve. Ann. Statist. 28 1105-1127.
    • (2000) Ann. Statist. , vol.28 , pp. 1105-1127
    • Genovese, C.1    Wasserman, L.2
  • 9
    • 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
  • 11
    • 0034164796 scopus 로고    scopus 로고
    • Convergence rates of posterior distributions
    • GHOSAL, S., GHOSH, J. K. and VAN DER VAART, A. W. (2000). Convergence rates of posterior distributions. Ann. Statist. 28 500-531.
    • (2000) Ann. Statist. , vol.28 , pp. 500-531
    • Ghosal, S.1    Ghosh, J.K.2    Van Der Vaart, A.W.3
  • 14
    • 0007258285 scopus 로고
    • An estimate of the density of a distribution belonging to a class of entire functions
    • in Russian
    • IBRAGIMOV, I. A. and KHASMINSKII, R. Z. (1982). An estimate of the density of a distribution belonging to a class of entire functions. Theory Probab. Appl. 27 514-524 (in Russian).
    • (1982) Theory Probab. Appl. , vol.27 , pp. 514-524
    • Ibragimov, I.A.1    Khasminskii, R.Z.2
  • 15
    • 0000624821 scopus 로고
    • ε-entropy and ε-capacity of sets in function spaces
    • KOLMOGOROV, A. N. and TIHOMIROV. 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 (1959) Uspekhi Mat. Nauk 14 3-86.]
    • (1961) Amer. Math. Soc. Transl. Ser. 2 , vol.17 , pp. 277-364
    • Kolmogorov, A.N.1    Tihomirov, V.M.2
  • 16
    • 0003179644 scopus 로고
    • KOLMOGOROV, A. N. and TIHOMIROV. 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 (1959) Uspekhi Mat. Nauk 14 3-86.]
    • (1959) Uspekhi Mat. Nauk , vol.14 , pp. 3-86
  • 18
    • 0001876649 scopus 로고
    • On a class of Bayesian nonparametric estimates I: Density estimates
    • LO, A. Y. (1984). On a class of Bayesian nonparametric estimates I: Density estimates. Ann. Statist. 12 351-357.
    • (1984) Ann. Statist. , vol.12 , pp. 351-357
    • Lo, A.Y.1
  • 21
    • 0000599677 scopus 로고    scopus 로고
    • Mixtures of distributions: Inference and estimation
    • W. Gilks, S. Richardson and D. Spiegelhalter, eds. Chapman and Hall, London
    • ROBERT, C. (1996). Mixtures of distributions: inference and estimation. In Markov Chain Monte Carlo in Practice (W. Gilks, S. Richardson and D. Spiegelhalter, eds.) 441-464. Chapman and Hall, London.
    • (1996) Markov Chain Monte Carlo in Practice , pp. 441-464
    • Robert, C.1
  • 22
    • 0000198157 scopus 로고
    • Semiparametric estimation of normal mixture densities
    • ROEDER, K. (1992). Semiparametric estimation of normal mixture densities. Ann. Statist. 20 929-943.
    • (1992) Ann. Statist. , vol.20 , pp. 929-943
    • Roeder, K.1
  • 23
    • 21744460005 scopus 로고    scopus 로고
    • Practical Bayesian density estimation using mixtures of normals
    • ROEDER, K. and WASSERMAN, L. (1997). Practical Bayesian density estimation using mixtures of normals. J. Amer. Statist. Assoc. 92 894-902.
    • (1997) J. Amer. Statist. Assoc. , vol.92 , pp. 894-902
    • Roeder, K.1    Wasserman, L.2
  • 26
    • 0035539848 scopus 로고    scopus 로고
    • Rates of convergence of posterior distributions
    • SHEN, X. and WASSERMAN, L. (2001). Rates of convergence of posterior distributions. Ann. Statist. 29 687-714.
    • (2001) Ann. Statist. , vol.29 , pp. 687-714
    • Shen, X.1    Wasserman, L.2
  • 27
    • 21844489169 scopus 로고
    • Convergence rate of sieve estimates
    • SHEN, X. and WONG, W. H. (1994). Convergence rate of sieve estimates. Ann. Statist. 22 580-615.
    • (1994) Ann. Statist. , vol.22 , pp. 580-615
    • Shen, X.1    Wong, W.H.2
  • 28
    • 21144465429 scopus 로고
    • Hellinger consistency of certain nonparametric maximum likelihood estimators
    • VAN DE GEER, S. (1993). Hellinger consistency of certain nonparametric maximum likelihood estimators. Ann. Statist. 21 14-44.
    • (1993) Ann. Statist. , vol.21 , pp. 14-44
    • De Van Geer, S.1
  • 29
    • 0000073296 scopus 로고    scopus 로고
    • Rates of convergence for the maximum likelihood estimator in mixture models
    • VAN DE GEER, S. (1996). Rates of convergence for the maximum likelihood estimator in mixture models. J. Nonparametr. Statist. 6 293-310.
    • (1996) J. Nonparametr. Statist. , vol.6 , pp. 293-310
    • De Van Geer, S.1
  • 32
    • 0003049326 scopus 로고
    • Modeling with mixtures
    • J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds. Oxford Univ. Press
    • WEST, M. (1992). Modeling with mixtures. In Bayesian Statistics 4 (J. M. Bernardo, J. O. Berger, A. P. Dawid and A. F. M. Smith, eds.) 503-524. Oxford Univ. Press.
    • (1992) Bayesian Statistics 4 , pp. 503-524
    • West, M.1
  • 33
    • 0002612391 scopus 로고
    • Hierarchical priors and mixture models, with applications in regression and density estimation
    • P. R. Freeman and A. F. M. Smith, eds. Wiley, New York
    • WEST, M., MULLER, P. and ESCOBAR, M. D. (1994). Hierarchical priors and mixture models, with applications in regression and density estimation. In Aspects of Uncertainty: A Tribute to D. V. Lindley (P. R. Freeman and A. F. M. Smith, eds.) 363-386. Wiley, New York.
    • (1994) Aspects of Uncertainty: A Tribute to D. V. Lindley , pp. 363-386
    • West, M.1    Muller, P.2    Escobar, M.D.3
  • 34
    • 21844517288 scopus 로고
    • Probability inequalities for likelihood ratios and convergence rates of sieve MLEs
    • WONG, W. H. and SHEN, X. (1995). Probability inequalities 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


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