Extremal attractors of Liouville copulas

Liouville copulas, which were introduced in McNeil and Neslehova (2010), are asymmetric generalizations of the ubiquitous Archimedean copula class. They are the dependence structures of scale mixtures of Dirichlet distributions, also called Liouville distributions. In this paper, the limiting extreme-value copulas of Liouville copulas and of their survival counterparts are derived. The limiting max-stable models, termed here the scaled extremal Dirichlet, are new and encompass several existing classes of multivariate max-stable distributions, including the logistic, negative logistic and extremal Dirichlet. As shown herein, the stable tail dependence function and angular density of the scaled extremal Dirichlet model have a tractable form, which in turn leads to a simple de Haan representation. The latter is used to design efficient algorithms for unconditional simulation based on the work of Dombry, Engelke and Oesting (2015) and to derive tractable formulas for maximum-likelihood inference. The scaled extremal Dirichlet model is illustrated on river flow data of the river Isar in southern Germany.Comment: 30 pages including supplementary material, 6 figure

A Bayesian view of doubly robust causal inference

In causal inference confounding may be controlled either through regression adjustment in an outcome model, or through propensity score adjustment or inverse probability of treatment weighting, or both. The latter approaches, which are based on modelling of the treatment assignment mechanism and their doubly robust extensions have been difficult to motivate using formal Bayesian arguments, in principle, for likelihood-based inferences, the treatment assignment model can play no part in inferences concerning the expected outcomes if the models are assumed to be correctly specified. On the other hand, forcing dependency between the outcome and treatment assignment models by allowing the former to be misspecified results in loss of the balancing property of the propensity scores and the loss of any double robustness. In this paper, we explain in the framework of misspecified models why doubly robust inferences cannot arise from purely likelihood-based arguments, and demonstrate this through simulations. As an alternative to Bayesian propensity score analysis, we propose a Bayesian posterior predictive approach for constructing doubly robust estimation procedures. Our approach appropriately decouples the outcome and treatment assignment models by incorporating the inverse treatment assignment probabilities in Bayesian causal inferences as importance sampling weights in Monte Carlo integration.Comment: Author's original version. 21 pages, including supplementary materia

Objectif privilégié de l’entreprise

Dans cet article, l’auteur explique comment la maximisation du profit représente pour les entreprises économiques le critère de décision le plus opérationnel, tout en reconnaissant l'existence de multiples sous-objectifs ou contraintes. Cet objectif privilégié constitue le meilleur dénominateur commun pour tous les agents économiques de l’entreprise, à la condition, bien entendu, de se situer à un niveau moyen d'abstraction.Most of the firm's specialists teach and have taught that profit maximization is a fundamental assumption in the micro-economic theory. Following the economic culture prevailing in a capitalist society, one must admit in addition to this fundamental assumption the fact that a firm seeks profits. However the results of many surveys conducted among top firm executives led to the conclusion that most of them do not seek profit maximization but the sales volume, the share of the market, etc. It is even pretended that one single firm seeks for many objectives at the same time.However it seems evident that only one objective can represent the final criterion of decision. It is called the basic objective which is pretended not to be different from profit maximization. Certainly the existence of sub-objectives or constraints to be respected by the firm in evaluating them in the terms of the basic objective is recognized.This proposition is deduced from three main assumptions. In the first place nobody can deny the fact that a serious executive wishes to act rationaly i.e. to optimize its decisions. In the second place, he needs to situate himself at a medium level of abstraction in a step of the decision-making process. He cannot only consider profit maximization : neither can he get lost in the detail of each specific decision. Finally, in order to be sufficiently operational, the basic objective must be the best common denominator to all the other objectives which then become sub-objectives or contraints.Those three assumptions can allow the deduction of the following proposition : profit maximization seems to be the best basic objective of the firm. In fact, only profit represents the result of all the economic activities of a firm