A classification point-of-view about conditional Kendall's tau

TL;DR

This paper reformulates the estimation of conditional Kendall's tau as a classification problem, developing theoretical properties, algorithms, and applying them to financial data to assess dependence structures.

Contribution

It introduces a novel classification-based approach for estimating conditional Kendall's tau, including theoretical guarantees and adaptation of machine learning algorithms.

Findings

Proves consistency and asymptotic normality of estimators.

Demonstrates effectiveness of machine learning methods in estimation.

Applies methods successfully to stock index data.

Abstract

We show how the problem of estimating conditional Kendall's tau can be rewritten as a classification task. Conditional Kendall's tau is a conditional dependence parameter that is a characteristic of a given pair of random variables. The goal is to predict whether the pair is concordant (value of $1$) or discordant (value of $-1$) conditionally on some covariates. We prove the consistency and the asymptotic normality of a family of penalized approximate maximum likelihood estimators, including the equivalent of the logit and probit regressions in our framework. Then, we detail specific algorithms adapting usual machine learning techniques, including nearest neighbors, decision trees, random forests and neural networks, to the setting of the estimation of conditional Kendall's tau. Finite sample properties of these estimators and their sensitivities to each component of the data-generating process are assessed in a simulation study. Finally, we apply all these estimators to a dataset of European stock indices.