Optimal Designs for Copula Models

TL;DR

This paper develops optimal experimental design methods for copula models, enabling more efficient parameter estimation and robustness checks across different copula types in applied statistics.

Contribution

It introduces an equivalence theorem for bivariate copula models, facilitating the creation of efficient design algorithms and practical efficiency assessments.

Findings

Design efficiency can be significantly improved with optimized experiments.

The equivalence theorem enables quick checks of design optimality.

Comparisons show robustness of parameter estimates across copula types.

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.