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Deviation inequalities for stochastic approximation by averaging. Stoch Process Their Appl 2022. [DOI: 10.1016/j.spa.2022.07.002] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/20/2022]
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Riekert A. Convergence rates for empirical measures of Markov chains in dual and Wasserstein distances. Stat Probab Lett 2022. [DOI: 10.1016/j.spl.2022.109605] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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3
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Garnier R, Langhendries R. Concentration inequalities for non-causal random fields. Electron J Stat 2022. [DOI: 10.1214/22-ejs1992] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
Affiliation(s)
- Rémy Garnier
- CY University - AGM UMR 8088, 2 Bd. Adolphe Chauvin. 95000 Cergy-Pontoise, France
| | - Raphaël Langhendries
- University Paris 1 Panthéon-Sorbonne - SAMM, 90, rue de Tolbiac 75013 PARIS CEDEX 13 - France
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Lei J. Convergence and concentration of empirical measures under Wasserstein distance in unbounded functional spaces. BERNOULLI 2020. [DOI: 10.3150/19-bej1151] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Abstract
We propose a “decomposition method” to prove non-asymptotic bound for the convergence of empirical measures in various dual norms. The main point is to show that if one measures convergence in duality with sufficiently regular observables, the convergence is much faster than for, say, merely Lipschitz observables. Actually, assuming s derivatives with s > d∕2 (d the dimension) ensures an optimal rate of convergence of 1/√n (n the number of samples). The method is flexible enough to apply to Markov chains which satisfy a geometric contraction hypothesis, assuming neither stationarity nor reversibility, with the same convergence speed up to a power of logarithm factor. Our results are stated as controls of the expected distance between the empirical measure and its limit, but we explain briefly how the classical method of bounded difference can be used to deduce concentration estimates.
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Kloeckner B. Effective Berry–Esseen and concentration bounds for Markov chains with a spectral gap. ANN APPL PROBAB 2019. [DOI: 10.1214/18-aap1438] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Large and moderate deviations
for the left random walk on GLd(R). LATIN AMERICAN JOURNAL OF PROBABILITY AND MATHEMATICAL STATISTICS 2017. [DOI: 10.30757/alea.v14-26] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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