A0563
Title: Towards a universal representation of statistical dependence
Authors: Gery Geenens - University of New South Wales (Australia) [presenting]
Abstract: Dependence is undoubtedly a central concept in statistics. Though, it proves difficult to locate in the literature a formal definition which goes beyond a self-evident interpretation of "dependence = non-independence", which quickly proves inadequate. For example, quantifying dependence between two variables appears essential in many situations; yet, if dependence is to be quantifiable, then the above non-independence definition falls short, and this is without any obvious substitute. This absence has allowed the term "dependence" and its declination to be used vaguely and indiscriminately for qualifying a variety of disparate notions, leading to numerous incongruities. Arguing that research on such a fundamental topic would benefit from a slightly more rigid framework, this work suggests a general definition of the dependence between two random variables defined on the same probability space. Natural enough for aligning with intuition, that definition is still sufficiently precise for allowing unequivocal identification of a "universal" representation of the dependence structure of any bivariate distribution regardless of its nature (discrete, continuous, mixed, hybrid). Links between this representation and familiar concepts are highlighted. The role of copulas will also be discussed from that perspective, showing that copulas provide a sensible approach for analysing and modelling dependence in a continuous vector but cannot be justified outside that framework.
