Title: Quantifying the closeness to a set of random curves via the mean marginal likelihood
Authors: Cedric Rommel - INRIA, Polytechnique (France) [presenting]
Frederic Bonnans - INRIA-Polytechnique (France)
Pierre Martinon - INRIA-Polytechnique (France)
Baptiste Gregorutti - Universite Pierre et Marie Curie (France)
Abstract: The problem of quantifying the closeness of a newly observed curve to a given sample of random functions is tackled, when it is supposed that they 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.