Adaptive estimation of the conditional intensity of marker-dependent counting processes

TL;DR

This paper introduces an adaptive estimator for the conditional intensity of marker-dependent counting processes, achieving optimal convergence rates and demonstrated through hazard estimation examples.

Contribution

It presents a novel adaptive estimator with proven optimal convergence rates for marker-dependent counting processes, using model selection techniques.

Findings

Estimator achieves optimal convergence rate.

Provides non-asymptotic risk bounds.

Illustrated in conditional hazard estimation context.

Abstract

We propose in this work an original estimator of the conditional intensity of a marker-dependent counting process, that is, a counting process with covariates. We use model selection methods and provide a non asymptotic bound for the risk of our estimator on a compact set. We show that our estimator reaches automatically a convergence rate over a functional class with a given (unknown) anisotropic regularity. Then, we prove a lower bound which establishes that this rate is optimal. Lastly, we provide a short illustration of the way the estimator works in the context of conditional hazard estimation.