A classification point-of-view about conditional Kendall's tau
This work addresses a statistical dependence estimation problem for researchers in statistics and machine learning, but it is incremental as it adapts existing methods to a specific parameter.
The paper tackles the problem of estimating conditional Kendall's tau by reframing it as a classification task, proving consistency and asymptotic normality for penalized estimators and adapting machine learning algorithms like random forests and neural networks, with applications to European stock indices.
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.