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...

Let (omega, beta) be a measurable space, An in B a sub-sigma-field and µn a random probability measure, n = 1. In various frameworks, one looks for a probability P on B such that µn is a regular conditional distribution for P given An for all n. Conditions for such a P to exist are given. The...

An urn contains balls of d = 2 colors. At each time n = 1, a ball is drawn and then replaced together with a random number of balls of the same color. Let An =diag (An,1, . . . ,An,d) be the n-th reinforce matrix. Assuming EAn,j = EAn,1 for all n and j, a few CLT s are available for such urns....

The increasing exposure to renewable energy has amplified the need for risk management in electricity markets. Electricity price risk poses a major challenge to market participants. We propose an approach to model and fore- cast electricity prices taking into account information on renewable...

The definition of vectors of dependent random probability measures is a topic of interest in applications to Bayesian statistics. They, indeed, represent dependent nonparametric prior distributions that are useful for modelling observables for which specific covariate values are known. In this...