Bayesian nonparametric models based on infinite mixtures of density kernels have been recently gaining in popularity due to their flexibility and feasibility of implementation even in complicated modeling scenarios. In economics, they have been particularly useful in estimating nonparametric...

Using a large deviations approach, Maximum A-Posteriori Probability (MAP) and Empirical Likelihood (EL) are shown to possess, under misspecification, an exclusive property of Bayesian consistency. Under conditions of consistency, regardless of prior the MAP estimator asymptotically coincides...

The consistency of the local kernel density estimator is proved. This nonparametric estimator is distinguished by its use of scaling matrices which are random and which may vary for each sample point. Its applications include adaptive construction of importance sampling functions.