A unifying framework for Bayesian analysis in discrete nonparametric settings is proposed. To this aim, a general class of nonparametric discrete prior distributions on an arbitrary sample space is introduced. The general structure of the posterior and predictive distributions and an explicit...

We show that the cumulative distribution function corresponding to a kernel density estimator with optimal bandwidth lies outside any confidence interval, around the empirical distribution function, with probability tending to 1 as the sample size increases.

In many spatial and spatial-temporal models, and more generally in models with complex dependencies, it may be too difficult to carry out full maximum-likelihood (ML) analysis. Remedies include the use of pseudo-likelihood (PL) and quasi-likelihood (QL) (also called the composite likelihood)....

To test if a density "f" is equal to a specified "f"₀, one knows by the Neyman-Pearson lemma the form of the optimal test at a specified alternative "f"₁. Any non-parametric density estimation scheme allows an estimate of "f". This leads to estimated likelihood ratios. Properties are studied of...