Bio: M.J. Frank is an academic researcher. The author has an hindex of 1, co-authored 1 publication(s) receiving 524 citation(s).
TL;DR: This paper presents an introduction to inference for copula models, based on rank methods, by working out in detail a small, fictitious numerical example, the various steps involved in investigating the dependence between two random variables and in modeling it using copulas.
Abstract: This paper presents an introduction to inference for copula models, based on rank methods. By working out in detail a small, fictitious numerical example, the writers exhibit the various steps involved in investigating the dependence between two random variables and in modeling it using copulas. Simple graphical tools and numerical techniques are presented for selecting an appropriate model, estimating its parameters, and checking its goodness-of-fit. A larger, realistic application of the methodology to hydrological data is then presented.
••01 Jan 2003
TL;DR: One main aim of this paper is to show that when addressing the problem of simulating dependent data arises naturally in Monte Carlo approaches to risk management knowledge of copulas and copula based dependence concepts is important, and also the usefulness of copula ideas in this approach torisk management.
01 Nov 2006
TL;DR: In this paper, the authors present a critical review of blanket tests for goodness-of-fit testing of copula models and suggest new ones, and conclude with a number of practical recommendations.
Abstract: Many proposals have been made recently for goodness-of-fit testing of copula models. After reviewing them briefly, the authors concentrate on "blanket tests", i.e.,Â those whose implementation requires neither an arbitrary categorization of the data nor any strategic choice of smoothing parameter, weight function, kernel, window, etc. The authors present a critical review of these procedures and suggest new ones. They describe and interpret the results of a large Monte Carlo experiment designed to assess the effect of the sample size and the strength of dependence on the level and power of the blanket tests for various combinations of copula models under the null hypothesis and the alternative. To circumvent problems in the determination of the limiting distribution of the test statistics under composite null hypotheses, they recommend the use of a double parametric bootstrap procedure, whose implementation is detailed. They conclude with a number of practical recommendations.
01 Jul 1985-Information Sciences
TL;DR: An extensive survey on fuzzy set-theoretic operations is provided, and the relevance of the theory of functional equations in the axiomatical construction of classes of such operations and the derivation of functional representations is emphasized.
Abstract: One of the most attractive features of fuzzy set theory is to provide a mathematical setting for the integration of subjective categories represented by membership functions. Indeed, a body of aggregation operations is already available, which may be useful in decision analysis, quantitative psychology and information processing. This paper provides an extensive survey on fuzzy set-theoretic operations, and emphasizes the relevance of the theory of functional equations in the axiomatical construction of classes of such operations and the derivation of functional representations. The second part is devoted to the application of fuzzy set theory to multifactorial evaluation. Some links between this approach and multiattribute utility theory are explored. Problems of modeling the importance of criteria, as well as of choosing a proper aggregation connective in a given situation, are also discussed.
01 Jan 1996
TL;DR: In this article, a class of parametric distributions with given margins and m(m? l)/2 dependence parameters, which is based on iteratively mixing conditional distributions, is derived.
Abstract: A class of ra-variate distributions with given margins and m(m ? l)/2 dependence parameters, which is based on iteratively mixing conditional distributions, is derived. The family of multivariate normal distributions is a special case. The motivation for the class is to get parametric families that have m(m ? l)/2 dependence parameters and properties that the family of multivariate normal distributions does not have. Properties of the class are studied, with details for (i) conditions for bivariate tail dependence and non-trivial limiting multivariate extreme value distributions and (ii) range of dependence for a bivariate measure of association such as Kendall's tau.