Adaptive Convergence Rates of a Dirichlet Process Mixture of Multivariate Normals

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Tokdar, Surya T.;
  • Subject: Mathematics - Statistics Theory | Statistics - Methodology

It is shown that a simple Dirichlet process mixture of multivariate normals offers Bayesian density estimation with adaptive posterior convergence rates. Toward this, a novel sieve for non-parametric mixture densities is explored, and its rate adaptability to various sm... View more
  • References (18)
    18 references, page 1 of 2

    Chung, Y. and D. B. Dunson (2009). Nonparametric Bayes conditional distribution modeling with variable selection. Journal of the American Statistical Association 104, 1646-1660.

    de Jonge, R. and J. H. van Zanten (2010). Adaptive nonparametric bayesian inference using location-scale mixture priors. The Annals of Statistics 38, 3300-3320.

    Dunson, D. B. and J. H. Park (2008). Kernel stick-breaking processes. Biometrika 95, 307-323.

    Ferguson, T. (1973). Bayesian analysis of some nonparametric problems. Annals of Statistics 1, 209-230.

    Ghosal, S., J. K. Ghosh, and R. V. Ramamoorthi (1999). Posterior consistency of Dirichlet mixtures in density estimation. The Annals of Statistics 27, 143-158.

    Ghosal, S., J. K. Ghosh, and A. W. van der Vaart (2000). Convergence rates of posterior distributions. The Annals of Statistics 28, 500-531.

    Ghosal, S. and A. W. van der Vaart (2001). Entropies and rates of convergence for maximum likelihood and Bayes estimation for mixtures of normal densities. The Annals of Statistics 29, 1233-1263.

    Ghosal, S. and A. W. van der Vaart (2007). Posterior convergence rates of Dirichlet mixtures at smooth densities. The Annals of Statistics 35, 697-723.

    Huang, T.-M. (2004). Convergence rates for posterior distributions and adaptive estimation. The Annals of Statistics 32, 1556-1593.

    Ibragimov, I. A. and R. Z. Khas'minskii (1983). Estimation of distribution density. Journal of Mathematical Science 21, 40-57.

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