Estimation of the density of a determinantal process

TL;DR

This paper introduces a new estimator for the density of a determinantal process using aggregation and robust testing, providing non-asymptotic risk bounds and convergence rates.

Contribution

It presents a novel aggregation-based estimation method for determinantal process densities with theoretical risk bounds and convergence guarantees.

Findings

Non-asymptotic risk bounds established

Uniform convergence rates derived

Effective estimator constructed for determinantal processes

Abstract

We consider the problem of estimating the density $\Pi$ of a determinantal process $N$ from the observation of $n$ independent copies of it. We use an aggregation procedure based on robust testing to build our estimator. We establish non-asymptotic risk bounds with respect to the Hellinger loss and deduce, when $n$ goes to infinity, uniform rates of convergence over classes of densities $\Pi$ of interest.