Weak transport inequalities and applications to exponential and oracle inequalities

Olivier Wintenberger

doi:10.1214/ejp.v20-3558

Weak transport inequalities and applications to exponential and oracle inequalities

Olivier Wintenberger

Institut for Matematiske Fag

3 Citationer (Scopus)

Abstract

We study the dimension-free inequalities, see Talagrand [49], for non-product measures extending Marton’s [39] weak transport from the Hamming distance to other metrics. The Euclidian norm is proved to be appropriate for dealing with non-product measures associated with classical time series. Our approach to address dependence, based on coupling of trajectories, weakens previous contractive arguments used in [20] and [41]. Following Bobkov-Götze’s [10] approach, we derive sub-Gaussianity and a convex Poincaré inequality for non-product measures that are not uniformly mixing, extending the Samson’s [48] results. Such dimension-free inequalities are useful for applications in statistics. Expressing the concentration properties of the ordinary least squares estimator as a weak transport problem, we obtain new oracle inequalities with fast rates of convergence for classical time series models.

Originalsprog	Engelsk
Artikelnummer	114
Tidsskrift	Electronic Journal of Probability
Vol/bind	20
Antal sider	27
ISSN	1083-6489
DOI	https://doi.org/10.1214/ejp.v20-3558
Status	Udgivet - 2015

Adgang til dokumentet

10.1214/ejp.v20-3558

Citationsformater

@article{b1895cca56794e99b07b3be3638f2a8c,

title = "Weak transport inequalities and applications to exponential and oracle inequalities",

abstract = "We study the dimension-free inequalities, see Talagrand [49], for non-product measures extending Marton{\textquoteright}s [39] weak transport from the Hamming distance to other metrics. The Euclidian norm is proved to be appropriate for dealing with non-product measures associated with classical time series. Our approach to address dependence, based on coupling of trajectories, weakens previous contractive arguments used in [20] and [41]. Following Bobkov-G{\"o}tze{\textquoteright}s [10] approach, we derive sub-Gaussianity and a convex Poincar{\'e} inequality for non-product measures that are not uniformly mixing, extending the Samson{\textquoteright}s [48] results. Such dimension-free inequalities are useful for applications in statistics. Expressing the concentration properties of the ordinary least squares estimator as a weak transport problem, we obtain new oracle inequalities with fast rates of convergence for classical time series models.",

author = "Olivier Wintenberger",

year = "2015",

doi = "10.1214/ejp.v20-3558",

language = "English",

volume = "20",

journal = "Electronic Journal of Probability",

issn = "1083-6489",

publisher = "Institute of Mathematical Statistics",

}

TY - JOUR

T1 - Weak transport inequalities and applications to exponential and oracle inequalities

AU - Wintenberger, Olivier

PY - 2015

Y1 - 2015

N2 - We study the dimension-free inequalities, see Talagrand [49], for non-product measures extending Marton’s [39] weak transport from the Hamming distance to other metrics. The Euclidian norm is proved to be appropriate for dealing with non-product measures associated with classical time series. Our approach to address dependence, based on coupling of trajectories, weakens previous contractive arguments used in [20] and [41]. Following Bobkov-Götze’s [10] approach, we derive sub-Gaussianity and a convex Poincaré inequality for non-product measures that are not uniformly mixing, extending the Samson’s [48] results. Such dimension-free inequalities are useful for applications in statistics. Expressing the concentration properties of the ordinary least squares estimator as a weak transport problem, we obtain new oracle inequalities with fast rates of convergence for classical time series models.

AB - We study the dimension-free inequalities, see Talagrand [49], for non-product measures extending Marton’s [39] weak transport from the Hamming distance to other metrics. The Euclidian norm is proved to be appropriate for dealing with non-product measures associated with classical time series. Our approach to address dependence, based on coupling of trajectories, weakens previous contractive arguments used in [20] and [41]. Following Bobkov-Götze’s [10] approach, we derive sub-Gaussianity and a convex Poincaré inequality for non-product measures that are not uniformly mixing, extending the Samson’s [48] results. Such dimension-free inequalities are useful for applications in statistics. Expressing the concentration properties of the ordinary least squares estimator as a weak transport problem, we obtain new oracle inequalities with fast rates of convergence for classical time series models.

U2 - 10.1214/ejp.v20-3558

DO - 10.1214/ejp.v20-3558

M3 - Journal article

SN - 1083-6489

VL - 20

JO - Electronic Journal of Probability

JF - Electronic Journal of Probability

M1 - 114

ER -

Weak transport inequalities and applications to exponential and oracle inequalities

Abstract

Adgang til dokumentet

Fingeraftryk

Citationsformater