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Adaptive Bayesian multivariate density estimation with Dirichlet mixtures
2013
Biometrika
We show that rate-adaptive multivariate density estimation can be performed using Bayesian methods based on Dirichlet mixtures of normal kernels with a prior distribution on the kernel's covariance matrix parameter. We derive sufficient conditions on the prior specification that guarantee convergence to a true density at a rate that is optimal minimax for the smoothness class to which the true density belongs. No prior knowledge of smoothness is assumed. The sufficient conditions are shown to
doi:10.1093/biomet/ast015
fatcat:wqwco4cjbrbi5podanio56juji