  This paper develops nonparametric estimation for discrete choice models based
on the mixed multinomial logit (MMNL) model. It has been shown that MMNL models
encompass all discrete choice models derived under the assumption of random
utility maximization, subject to the identification of an unknown distribution
$G$. Noting the mixture model description of the MMNL, we employ a Bayesian
nonparametric approach, using nonparametric priors on the unknown mixing
distribution $G$, to estimate choice probabilities. We provide an important
theoretical support for the use of the proposed methodology by investigating
consistency of the posterior distribution for a general nonparametric prior on
the mixing distribution. Consistency is defined according to an $L_1$-type
distance on the space of choice probabilities and is achieved by extending to a
regression model framework a recent approach to strong consistency based on the
summability of square roots of prior probabilities. Moving to estimation,
slightly different techniques for non-panel and panel data models are
discussed. For practical implementation, we describe efficient and relatively
easy-to-use blocked Gibbs sampling procedures. These procedures are based on
approximations of the random probability measure by classes of finite
stick-breaking processes. A simulation study is also performed to investigate
the performance of the proposed methods.
