This note considers a standard multinomial choice model. It is shown that if the distribution of additive utility shocks has a density, then the mapping from de- terministic components of utilities to choice probabilities is surjective. In other words, any vector of choice probabilities can be...

This paper considers Bayesian nonparametric estimation of conditional densities by countable mixtures of location-scale densities with covariate dependent mixing probabilities. The mixing probabilities are modeled in two ways. First, we consider finite covariate dependent mixture models, in...

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...