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

By Subhashis Ghosal, A. van der Vaart. 2001

355 citations recorded by the source corpus.

Subfields: Artificial Intelligence, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/52413b3078a2c877ec588e39726f539038eee1c5

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In Statistics and Probability

Citations in the corpus

Posterior convergence rates of Dirichlet mixtures at smooth densities (2007, background): “[9]) is the presence of the factor aτ−1.”
Adaptive Bayesian density estimation with location-scale mixtures (2010, background): “They are straightforward extensions of the corresponding results for normal mixtures, contained in lemma 3.1 of [14] and lemma 2 of [13].”
Rates of contraction for posterior distributions in Lr-metrics, 1 ≤ r ≤ ∞ (2011, background): “1 in [13] that for εn = (logn) κ/ √ n,κ≥ 1, the small-ball estimate in condition (2) of Theorem 2 is satisfied.”
Direct importance estimation for covariate shift adaptation (2008, background): “In many real-world applications such as robot control (Sutton and Barto 1998; Shelton 2001; Hachiya et al. 2008), bioinformatics (Baldi and Brunak 1998; Borgwardt et al.”
Misspecification in infinite-dimensional Bayesian statistics (2006, background): “nger distance is bounded above bythe L 1-norm,theassumption implies that d2(P F 1 ,P F2 )≤C 2 1kP F1 −P F2k 1. Hence, for all ε >0, we have N(C 1ε,P,d) ≤ N(ε2,P,k·k 1). As a result of Lemma 3.3 in [9], there exists a constant C 2 >0 such that kP F1 −P F2k 1 ≤C 2 2kP F1 −P F2k∞ max ( 1,M, s log”
Bayesian regression tree ensembles that adapt to smoothness and sparsity (2017, methodology): “First, we state an extension of Lemma 3.1 of Ghosal and Van Der Vaart (2001) from dimension one to dimension d , and from the Gaussian kernel to any kernel K satisfying Assumption G. Lemma 6.”
Convergence rates of posterior distributions for non-i.i.d. observations (2007, background): “The following result, generalizing Theorem 2.4 of Ghosal, Ghosh and van der Vaart [14] for the i.i.d. case, bounds the rate of posterior convergence.”
Convergence rates for Bayesian density estimation of infinite-dimensional exponential families (2006, background): “1 in [15], page 1239 (see also Theorem 2.”
Rates of convergence for the posterior distributions of mixtures of betas and adaptive nonparamatric estimation of the density (2010, methodology): “The papers [4, 5] and [15] study the concentration rate of the posterior distribution under Dirichlet mixtures of Gaussian priors, and Ghosal [3] considers the Bernstein polynomial’s case, that is, the mixture of Beta distribution with fixed parameters.”