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Norets, Andriy
Pelenis, Justinas
Year of Publication: 
Series/Report no.: 
IHS Economics Series 342
We consider nonparametric estimation of a mixed discrete-continuous distribution under anisotropic smoothness conditions and possibly increasing number of support points for the discrete part of the distribution. For these settings, we derive lower bounds on the estimation rates in the total variation distance. Next, we consider a nonparametric mixture of normals model that uses continuous latent variables for the discrete part of the observations. We show that the posterior in this model contracts at rates that are equal to the derived lower bounds up to a log factor. Thus, Bayesian mixture of normals models can be used for optimal adaptive estimation of mixed discretecontinuous distributions.
Bayesian nonparametrics
adaptive rates
minimax rates
posterior contraction
discretecontinuous distribution
mixed scale
mixtures of normal distributions
latent variables
Document Type: 
Working Paper
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