Reda Chhaibi (LJAD – Université Côte d’Azur)
Wednesday, 10 June 2026, 2pm
Title: On the fluctuations of rank-based estimators for sensitivity indices
Abstract:
A first goal is to advertise a new class of sensitivity estimators, which can be useful in a variety of contexts, including feature selection, detecting causality, computer code experiments, and fairness. The second goal is to present our contribution in understanding their fluctuations.
Given a bivariate random pair (X, Y), a basic question is how to estimate, from a single n-sample (Xᵢ, Yᵢ), quantities such as 𝔼[𝔼[Y | X]²]. More generally, sensitivity indices quantify the possibly nonlinear influence of an input variable X on an output variable Y. A classical example is the Sobol’ index:
Var(𝔼[Y | X]) / Var(Y) ∈ [0, 1].
Following groundbreaking work of Chatterjee, rank-based estimators have become a natural tool in this setting: they are distribution-free and can be computed in O(n log n) time.
After introducing the topic, I will present recent results establishing Gaussian fluctuations for two important examples, the Sobol’ index and the Cramér–von Mises index. The proofs are based on martingale arguments, and require only minimal regularity assumptions. They also yield explicit formulas for the asymptotic variance that appear to be new.
This talk is based on joint work with Fabrice Gamboa and Clément Pellegrini, available on arXiv:2603.22611.
