Aggregation functions: an approach using copulae

In this paper we present the extension of the copula approach to aggregation functions. In fact we want to focus on a class of aggregation functions and present them in the multilinear form with marginal copulae. Moreover, we define the joint aggregation density function.

Aggregation functions: Means

The two-parts state-of-art overview of aggregation theory summarizes the essential information concerning aggregation issues. Overview of aggregation properties is given, including the basic classification of aggregation functions. In this first part, the stress is put on means, i.e., averaging aggregation functions, both with fixed arity (n-ary means) and with open arity (extended means).

Mixed Marginal Copula Modeling

This article extends the literature on copulas with discrete or continuous marginals to the case where some of the marginals are a mixture of discrete and continuous components. We do so by carefully defining the likelihood as the density of the observations with respect to a mixed measure. The treatment is quite general, although we focus focus on mixtures of Gaussian and Archimedean copulas. The inference is Bayesian with the estimation carried out by Markov chain Monte Carlo. We illustrate the methodology and algorithms by applying them to estimate a multivariate income dynamics model.Comment: 46 pages, 8 tables and 4 figure