a b s t r a c tA new kernel-type estimator of the conditional density is proposed. It is based on an efficient quantile transformation of the data. The proposed estimator, which is based on the copula representation, turns out to have a remarkable product form. Its large-sample properties are considered and comparisons in terms of bias and variance are made with competitors based on nonparametric regression. A comparative simulation study is also provided.

In this note, we elucidate some of the mathematical, statistical and epistemological issues involved in using copulas to model discrete data. We contrast the possible use of (nonparametric) copula methods versus the problematic use of parametric copula models. For the latter, we stress, among other issues, the possibility of obtaining impossible models, arising from model misspecification or unidentifiability of the copula parameter.

For this panel discussion, several distinguished re-A panel discussion on the theme of this report was organized for searchers have agreed to provide a critique of the aspect the 1991 IEEE Workshop on Directions in Automated CAD-Bused graph approach, and several other distinguished reVision. This report contains the revised comments of the panel searchers who are working in the aspect graph area have discussion paI%@XultS.

which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. AbstractThe main aim of this paper is to introduce the notion of risk excess measure, to analyze its properties, and to describe some basic construction methods. To compare the risk excess of one distribution Q w.r.t. a given risk distribution P, we apply the concept of hemi-metrics on the space of probability measures. This view of risk comparison has a natural basis in the extension of orderings and hemi-metrics on the underlying space to the level of probability measures. Basic examples of these kind of extensions are induced by mass transportation and by function class induced orderings. Our view towards measuring risk excess adds to the usually considered method to compare risks of Q and P by the values ρ(Q), ρ(P) of a risk measure ρ. We argue that the difference ρ(Q) − ρ(P) neglects relevant aspects of the risk excess which are adequately described by the new notion of risk excess measure. We derive various concrete classes of risk excess measures and discuss corresponding ordering and measure extension properties.

a b s t r a c tFor a vector X with a purely discrete multivariate distribution, we give simple short proofs of uniform a.s. convergence on their whole domain of two versions of genuine empirical copula functions, obtained either via probabilistic continuation, i.e. kernel smoothing, or via the distributional transform. These results give a positive answer to some delicate issues related to the convergence of copula functions in the discrete case. They are obtained under the very weak hypothesis of ergodicity of the sample, a framework which encompasses most types of serial dependence encountered in practice. Moreover, they allow to derive, as simple corollaries, almost sure consistency results for some recent extensions of concordance measures attached to discrete vectors. The proofs are based on a maximal coupling construction of the empirical cdf, a result of independent interest.