# Non-parametric Archimedean generator estimation with implications for multiple testing

## TL;DR

This paper introduces two non-parametric estimators for Archimedean copula generators to improve multiple testing procedures, comparing their performance with traditional methods through simulations.

## Contribution

It proposes novel non-parametric estimators for Archimedean copula generators and evaluates their effectiveness in multiple testing scenarios.

## Key findings

- The estimators perform comparably to the true generator in simulations.
- The proposed methods can control the family-wise error rate effectively.
- Simulation results show potential advantages over Bonferroni correction.

## Abstract

In multiple testing, the family-wise error rate can be bounded under some conditions by the copula of the test statistics. Assuming that this copula is Archimedean, we consider two non-parametric Archimedean generator estimators. More specifically, we use the non-parametric estimator from Genest et al. (2011) and a slight modification thereof. In simulations, we compare the resulting multiple tests with the Bonferroni test and the multiple test derived from the true generator as baselines.