Abstract
Copula modelling has in the past decade become a standard tool in many areas of applied statistics. However, a largely neglected aspect concerns the design of related experiments. Particularly the issue of whether the estimation of copula parameters can be enhanced by optimizing experimental conditions and how robust all the parameter estimates for the model are with respect to the type of copula employed. In this paper an equivalence theorem for (bivariate) copula models is provided that allows formulation of efficient design algorithms and quick checks of whether designs are optimal or at least efficient. Some examples illustrate that in practical situations considerable gains in design efficiency can be achieved. A natural comparison between different copula models with respect to design efficiency is provided as well.
Highlights
Due to their flexibility in describing dependencies and the possibility of separating marginal and joint effects copula models have become a popular device for coping with multivariate data. in many areas of applied statistics eg. for insurances,[1] econometrics,[2] medicine,[3] marketing,[4] spatial extreme events,[5] time series analysis,[6] even sports [7] and in finance.[8]
The design question for copula parameter estimation has to our knowledge just been raised in [12], where a bruteforce simulated annealing optimization was employed for the solution of a specific problem
We need to quantify the amount of information on both sets of parameters α and β respectively from the regression experiment embodied in the Fisher information matrix, which for an elemental information at a particular control x in the sense of Atkinson et al [15] is a (k + l) × (k + l) matrix defined as m(x, β, α) =
Summary
Due to their flexibility in describing dependencies and the possibility of separating marginal and joint effects copula models have become a popular device for coping with multivariate data. in many areas of applied statistics eg. for insurances,[1] econometrics,[2] medicine,[3] marketing,[4] spatial extreme events,[5] time series analysis,[6] even sports [7] and in finance.[8]. The design question for copula parameter estimation has to our knowledge just been raised in [12], where a bruteforce simulated annealing optimization was employed for the solution of a specific problem. Βk) is a certain unknown vector of marginal parameters to be estimated and ηi Let us call FYi (yi(x, β)) the marginal cumulative distributions of each Yi for all i = 1, . M and fY(y(x, β), α) the joint probability density function of the random vector Y, where α = Let FY be a joint cumulative distribution function (cdf) with marginal cdfs FY1 and FY2. If C is a 2-copula and FY1 and FY2 are distribution functions, the function FY given by Equation (2) is a joint distribution with marginals FY1 and FY2
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