# A Bayesian semiparametric Archimedean copula

## TL;DR

This paper introduces a Bayesian semiparametric approach to Archimedean copulas using a spline-based generator, enabling flexible modeling of dependence structures and hypothesis testing in a survival analysis framework.

## Contribution

It proposes a novel spline-based semiparametric generator for Archimedean copulas, with Bayesian inference and independence testing capabilities.

## Key findings

- The model covers the full range of Kendall's tau.
- Simulation studies validate the model's flexibility and accuracy.
- Application to real data demonstrates practical utility.

## Abstract

An Archimedean copula is characterised by its generator. This is a real function whose inverse behaves as a survival function. We propose a semiparametric generator based on a quadratic spline. This is achieved by modelling the first derivative of a hazard rate function, in a survival analysis context, as a piecewise constant function. Convexity of our semiparametric generator is obtained by imposing some simple constraints. The induced semiparametric Archimedean copula produces Kendall's tau association measure that covers the whole range $(-1,1)$. Inference on the model is done under a Bayesian approach and for some prior specifications we are able to perform an independence test. Properties of the model are illustrated with a simulation study as well as with a real dataset.