Weak transport inequalities and applications to exponential and oracle inequalities
| Autor: | Olivier Wintenberger |
|---|---|
| Přispěvatelé: | Laboratoire de Statistique Théorique et Appliquée (LSTA), Université Pierre et Marie Curie - Paris 6 (UPMC)-Centre National de la Recherche Scientifique (CNRS), University of Copenhagen = Københavns Universitet (UCPH), Université Pierre et Marie Curie - Paris 6 (UPMC), University of Copenhagen = Københavns Universitet (KU) |
| Jazyk: | angličtina |
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Discrete mathematics 010102 general mathematics Regular polygon Poincaré inequality Estimator Hamming distance 01 natural sciences Exponential function 010104 statistics & probability symbols.namesake concentration of measures Norm (mathematics) Ordinary least squares symbols Applied mathematics oracle inequalities 0101 mathematics Statistics Probability and Uncertainty Time series time series [MATH]Mathematics [math] transport inequalities Mathematics |
| Zdroj: | Electronic Journal of Probability Electronic Journal of Probability, 2015, 20, pp.114. ⟨10.1214/EJP.v20-3558⟩ Electron. J. Probab. Electronic Journal of Probability, Institute of Mathematical Statistics (IMS), 2015, 20, pp.114. ⟨10.1214/EJP.v20-3558⟩ |
| ISSN: | 1083-6489 |
| DOI: | 10.1214/EJP.v20-3558⟩ |
| Popis: | International audience; 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. |
| Databáze: | OpenAIRE |
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