Modern risk management calls for an understanding of stochastic dependence going beyond simple linear correlation. This paper deals with the static (non-time-dependent) case and emphasizes the copula representation of dependence for a random vector. Linear correlation is a natural dependence measure for multivariate normally and, more generally, elliptically distributed risks but other dependence concepts like comonotonicity and rank correlation should also be understood by the risk management practitioner. Using counterexamples the falsity of some commonly held views on correlation is demonstrated; in general, these fallacies arise from the naive assumption that dependence properties of the elliptical world also hold in the non-elliptical world. In particular, the problem of finding multivariate models which are consistent with prespecified marginal distributions and correlations is addressed. Pitfalls are highlighted and simulation algorithms avoiding these problems are constructed. ...

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. The nonparametric and the nuisance parameter approaches to consistently testing statistical models are both attempts to estimate topological measures of distance between a parametric and a nonparametric fit, and neither dominates in experiments. This topological unification allows us to greatly extend the nuisance parameter approach. How and why the nuisance parameter approach works and how it can be extended bears closely on recent developments in artificial neural networks. Statistical content is provided by viewing specification tests with nuisance parameters as tests of hypotheses about Banach-valued random elements and applying the Banach Central Limit Theorem and Law of Iterated Logarithm, leading to simple procedures that can be used as a guide to when computationally more elaborate procedures may be warranted. 1. Introduction In testing whether or not a parametric statistical model is correctly specified, there are a number of apparently distinct approaches one might take. T...

In this paper we study occluding contour artifacts in the area-based stereo matching. These artifacts are false, although highly correlated responses of the matching operator to the occlusion boundary and cause the objects extend beyond their true boundaries in disparity maps. The effect is so strong that it cannot be ignored. Current matching methods do not attempt to avoid the problem. We show what is the physical phenomenon that gives rise to the artifacts and design a matching criterion that accommodates the presence of the occlusions as opposite to methods that identify and remove the artifacts. This approach leads to the problem of measurement contamination studied in statistics. We show that such problem is hard given finite computational resources, unless more independent measurements directly related to occluding contours is available. What can be achieved is the substantial reduction of the artifacts, especially for large matching templates. Reduced artifacts allow for easier...

We discuss two methods of making nonparametric Bayesian inference on probability measures subject to a partial stochastic ordering. The first method involves a nonparametric prior for a measure on partially ordered latent observations, and the second involves rejection sampling. Computational approaches are discussed for each method, and interpretations of prior and posterior information are discussed. An application is presented in which inference is made on the number of independently segregating quantitative trait loci present in an animal population.

Abstract. This paper proposes a general non-Gaussian Ornstein-Uhlenbeck model for a joint financial process based on marginal Lévy measures joined by a Lévy copula. Simulated processes then result from choices of marginal measures and Lévy copulas, with resulting statistics and inferences. Selected for analysis are the 3/2-stable and Gamma marginal Lévy measures, along with Clayton, Gumbel, and Complementary Gumbel Lévy versions of ordinary [probability] copulas, with the last two being here introduced. A relationship between the original coupled subordinated processes and the terminal dependency relationship between the simulated variables is observed and calibrated. Normal inverse Gaussian and tempered stable measures are also noted, as are additional Lévy copulas constructed from the Gumbel and Frank ordinary copulas, with some analysis and suggestion for using them in future research. 1.

Multivariate statistical analysis relies heavily on moment assumptions of second order and higher. With increasing interest in modeling with heavy tailed distributions, however, it is desirable to describe dispersion, skewness, and kurtosis of multivariate distributions under merely first order moment assumptions. Here we present a new method contributing toward this goal in both parametric and nonparametric settings. We extend the univariate Lmoments of Hosking (1990), which are analogues of central moments defined for all orders under merely a first moment assumption, by introducing a notion of “L-comoments ” similarly analogous to classical central moment notions of covariance, coskewness, and cokurtosis. For certain types of model, this yields correlational analysis not only coherent with classical correlation but also valid and meaningful under just first moment assumptions. We develop basic properties and estimators for L-comoments, illustrate Lcomoment matrices for several multivariate models, examine the behavior of multivariate L-moments as nonparametric descriptive measures in a sampling experiment with a heavy-tailed distribution, and consider certain extensions such as trimmed versions. Also, applications to financial risk analysis and to regional frequency analysis in environmental science are discussed.

Conference for helpful suggestions on an earlier version of the paper. THE ECONOMIC VALUE OF FLEXIBILITY

Abstract. The paper introduces the pyramid probability distribution through its density in two dimensions, and investigates its properties and those of its copula. The research focuses on ways in which the distribution demonstrates dependence between its variables, primarily as revealed by its copula and related functions. The distribution bears a close relationship to the normal distribution in that its density is constructed from it and has normal margins, but is not binormal. The paper presents a general theory of the pyramid distribution, including the presentation of a one-parameter and two-parameter families. 1.

Chen, Sean Chen, and Harry Sharma. We also benefited from discussions with our colleagues Ivan Brick, Oded Palmon, Emilio Venezian, and John Wald. We are particularly indebted to the anonymous referee and the editor, Paul Malatesta, for their valuable suggestions that greatly improve the paper. All errors are our own.