We consider properties of determinants of some random symmetric matrices issued from multivariate statistics: Wishart/Laguerre ensemble (sample covariance matrices), Uniform Gram ensemble (sample correlation matrices) and Jacobi ensemble (MANOVA). If n is the size of the sample, r ≤ n the number of variates and Xn,r such a matrix, a generalization of the Bartlett-type theorems gives a decomposi...

This paper explores the dynamic dependence properties of a Lévy process, the Variance Gamma, which has non Gaussian marginal features and non Gaussian dependence. In a static context, such a non Gaussian dependence should be represented via copulas. Copulas, however, are not able to capture the dynamics of dependence. By computing the distance between the Gaussian copula and the actual one, we ...

A review of Monte Carlo methods for approximating the high-dimensional integrals that arise in Bayesian statistical analysis. Emphasis is on the features of many Bayesian applications which make Monte Carlo methods especially appropriate, and on Monte Carlo variance-reduction techniques especially well suited to Bayesian applications. A generalized logistic regression example is used to illustr...

The method of characteristics (the averaging over the characteristic formula) and the weak-sense numerical integration of ordinary stochastic differential equations together with the Monte Carlo technique are used to propose numerical methods for linear stochastic partial differential equations (SPDEs). Their orders of convergence in the mean-square sense and in the sense of almost sure converg...

The maximum strain experienced by the thinnest segment of a non-uniform fiber governs fiber breakage, yet this maximum strain can not be obtained from a normal single fiber test. Only the average strain of the whole fiber specimen can be obtained from a normal single fiber tensile test. This study has examined the relationship between the average strain, the maximum strain and the degree of fib...

The Halton sequence is a well-known multi-dimensional low discrepancy sequence. In this paper, we propose a new method for randomizing the Halton sequence: we randomize the start point of each component of the sequence. This method combines the potential accuracy advantage of Halton sequence in multi-dimensional integration with the practical error estimation advantage of Monte Carlo methods. T...

Quasi-random (or low discrepancy) sequences are sequences for which the convergence to the uniform distribution on [0; 1)s occurs rapidly. Such sequences are used in quasi-Monte Carlo methods for which the convergence speed, with respect to the N first terms of the sequence, is in O(N 1(lnN)s), where s is the mathematical dimension of the problem considered. The disadvantage of these methods is...

The tail mean–variance model was recently introduced for use in risk management and portfolio choice; it involves a criterion that focuses on the risk of rare but large losses, which is particularly importantwhen losses have heavy-tailed distributions. If returns or losses follow a multivariate elliptical distribution, the use of risk measures that satisfy certain well-known properties is equiv...

This paper is concerned with applying importance sampling as a variance reduction tool for computing extreme quantiles. A central limit theorem is derived for each of four proposed importance sampling quantile estimators. EEciency comparisons are provided in a certain asymptotic setting, using ideas from large deviation theory.