Quantifying the closeness to a set of random curves via the mean marginal likelihood

¹ CMAP, Ecole Polytechnique, and Inria-Saclay, route de Saclay, 91128 Palaiseau, France.
² Safety Line, Tour Montparnasse, 33 Avenue du Maine, 75015 Paris, France.
³ Sorbonne Université (Paris 6), Laboratoire Jacques-Louis Lions, CNRS and Inria, équipe CAGE, 4 place Jussieu, BC 187 75252 Paris cedex 05, France.

^* Corresponding author: frederic.bonnans@inria.fr

Received: 23 April 2019
Accepted: 10 December 2020

Abstract

In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.