An elliptical copula model is a distribution function whose copula is that of an elliptical distribution. The tail dependence function in such a bivariate model has a parametric representation with two parameters: a tail parameter and a correlation parameter. The correlation parameter can be...

Tail dependence copulas provide a natural perspective from which one can study the dependence in the tail of a multivariate distribution. For Archimedean copulas with continuously differentiable generators, regular variation of the generator near the origin is known to be closely connected to...

Convergence of a sequence of bivariate Archimedean copulas to another Archimedean copula or to the comonotone copula is shown to be equivalent with convergence of the corresponding sequence of Kendall distribution functions. No extra differentiability conditions on the generators are needed

We extend the three-step generalized methods of moments (GMM) approach of Kapoor, Kelejian, and Prucha (2007), which corrects for spatially correlated errors in static panel data models, by introducing a spatial lag and a one-period lag of the dependent variable as additional explanatory...

Sequential bifurcation (or SB) is an efficient and effective factor-screening method; i.e., SB quickly identifies the important factors (inputs) in experiments with simulation models that have very many factors — provided the SB assumptions are valid. The specific SB assumptions are: (i) a...

This chapter surveys two methods for the optimization of real-world systems that are modelled through simulation. These methods use either linear regression metamodels, or Kriging (Gaussian processes). The metamodel type guides the design of the experiment; this design fixes the input...

This tutorial reviews the design and analysis of simulation experiments. These experiments may have various goals: validation, prediction, sensitivity analysis, optimization (possibly robust), and risk or uncertainty analysis. These goals may be realized through metamodels. Two types of...

In this chapter we present Kriging also known as a Gaussian process (GP) model which is a mathematical interpolation method. To select the input combinations to be simulated, we use Latin hypercube sampling (LHS); we allow uniform and non-uniform distributions of the simulation inputs. Besides...

We derive new statistical tests for leave-one-out cross-validation of Kriging models. Graphically, we present these tests as scatterplots augmented with confidence intervals. We may wish to avoid extrapolation, which we define as prediction of the output for a point that is a vertex of the...

This article uses a sequentialized experimental design to select simulation input combinations for global optimization, based on Kriging (also called Gaussian process or spatial correlation modeling); this Kriging is used to analyze the input/output data of the simulation model (computer code)....