Importance Sampling and Stratification for Copula Models

An importance sampling approach for sampling from copula models is introduced. The proposed algorithm improves Monte Carlo estimators when the functional of interest depends mainly on the behaviour of the underlying random vector when at least one of its components is large. Such problems often arise from dependence models in finance and insurance. The importance sampling framework we propose is particularly easy to implement for Archimedean copulas. We also show how the proposal distribution of our algorithm can be optimized by making a connection with stratified sampling. In a case study inspired by a typical insurance application, we obtain variance reduction factors sometimes larger than 1000 in comparison to standard Monte Carlo estimators when both importance sampling and quasi-Monte Carlo methods are used.NSERC, Grant 238959 NSERC, Grant 501

Cardiac remodeling and dysfunction in nephrotic syndrome

There is an increased incidence of heart disease in patients with chronic nephrotic syndrome (NS), which may be attributable to the malnutrition and activated inflammatory state accompanying the sustained proteinuria. In this study, we evaluated renal function, cardiac morphometry, contractile function, and myocardial gene expression in the established puromycin aminonucleoside nephrosis rat model of NS. Two weeks after aminonucleoside injection, there was massive proteinuria, decreased creatinine clearance, and a negative sodium balance. Skeletal and cardiac muscle atrophy was present and was accompanied by impaired left ventricular (LV) hemodynamic function along with decreased contractile properties of isolated LV muscle strips. The expression of selected cytokines and proteins involved in calcium handling in myocardial tissue was evaluated by real time polymerase chain reaction. This revealed that the expression of interleukin-1beta, tumor necrosis factor-alpha, and phospholamban were elevated, whereas that of cardiac sarco(endo)plasmic reticulum calcium pump protein was decreased. We suggest that protein wasting and systemic inflammatory activation during NS contribute to cardiac remodeling and dysfunction

Likelihood inference for Archimedean copulas in high dimensions under known margins

AbstractExplicit functional forms for the generator derivatives of well-known one-parameter Archimedean copulas are derived. These derivatives are essential for likelihood inference as they appear in the copula density, conditional distribution functions, and the Kendall distribution function. They are also required for several asymmetric extensions of Archimedean copulas such as Khoudraji-transformed Archimedean copulas. Availability of the generator derivatives in a form that permits fast and accurate computation makes maximum-likelihood estimation for Archimedean copulas feasible, even in large dimensions. It is shown, by large scale simulation of the performance of maximum likelihood estimators under known margins, that the root mean squared error actually decreases with both dimension and sample size at a similar rate. Confidence intervals for the parameter vector are derived under known margins. Moreover, extensions to multi-parameter Archimedean families are given. All presented methods are implemented in the R package nacopula and can thus be studied in detail