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.
Keywords: Density estimation, functional data analysis, trajectory discrimination, kernel density estimator
@article{PS_2021__25_1_1_0,
author = {Rommel, C\'edric and Fr\'ed\'eric Bonnans, J. and Gregorutti, Baptiste and Martinon, Pierre},
title = {Quantifying the closeness to a set of random curves \protect\emph{ via} the mean marginal likelihood},
journal = {ESAIM: Probability and Statistics},
pages = {1--30},
year = {2021},
publisher = {EDP-Sciences},
volume = {25},
doi = {10.1051/ps/2020028},
mrnumber = {4224732},
zbl = {1466.62288},
language = {en},
url = {https://www.numdam.org/articles/10.1051/ps/2020028/}
}
TY - JOUR AU - Rommel, Cédric AU - Frédéric Bonnans, J. AU - Gregorutti, Baptiste AU - Martinon, Pierre TI - Quantifying the closeness to a set of random curves via the mean marginal likelihood JO - ESAIM: Probability and Statistics PY - 2021 SP - 1 EP - 30 VL - 25 PB - EDP-Sciences UR - https://www.numdam.org/articles/10.1051/ps/2020028/ DO - 10.1051/ps/2020028 LA - en ID - PS_2021__25_1_1_0 ER -
%0 Journal Article %A Rommel, Cédric %A Frédéric Bonnans, J. %A Gregorutti, Baptiste %A Martinon, Pierre %T Quantifying the closeness to a set of random curves via the mean marginal likelihood %J ESAIM: Probability and Statistics %D 2021 %P 1-30 %V 25 %I EDP-Sciences %U https://www.numdam.org/articles/10.1051/ps/2020028/ %R 10.1051/ps/2020028 %G en %F PS_2021__25_1_1_0
Rommel, Cédric; Frédéric Bonnans, J.; Gregorutti, Baptiste; Martinon, Pierre. Quantifying the closeness to a set of random curves via the mean marginal likelihood. ESAIM: Probability and Statistics, Tome 25 (2021), pp. 1-30. doi: 10.1051/ps/2020028
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