Volume 25, 2021
|Page(s)||1 - 30|
|Published online||04 March 2021|
Quantifying the closeness to a set of random curves via the mean marginal likelihood
CMAP, Ecole Polytechnique, and Inria-Saclay, route de Saclay,
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: firstname.lastname@example.org
Accepted: 10 December 2020
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.
Mathematics Subject Classification: 62G07 / 62G05 / 62P30 / 62M09
Key words: Density estimation / functional data analysis / trajectory discrimination / kernel density estimator
© The authors. Published by EDP Sciences, SMAI 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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