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Exponential inequalities for sums of random vectors

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  • Yurinskii, V. V.
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    Abstract

    This paper presents some generalizations of S. N. Bernstein's exponential bounds on probabilities of large deviations to the vector case. Inequalities for probabilities of large deviations of sums of independent random vectors are derived under a Cramér's type restriction on the rate of growth of absolute moments of the summands. Estimates are obtained for random vectors with values in Banach space, Sharper bounds hold in the case of finite-dimensional Euclidean or separable Hilbert spaces.

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    File URL: http://www.sciencedirect.com/science/article/B6WK9-4CRM9B8-7B/2/4e1bbaf84d07611f30aaa9da9bff1a47
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 6 (1976)
    Issue (Month): 4 (December)
    Pages: 473-499

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    Handle: RePEc:eee:jmvana:v:6:y:1976:i:4:p:473-499

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    Related research

    Keywords: Sums of independent random vectors large deviations exponential bounds S. N. Bernstein's inequality Hilbert space Banach space;

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    Cited by:
    1. Dahmani, Abdelnasser & Ait Saidi, Ahmed & Bouhmila, Fatah & Aissani, Mouloud, 2009. "Consistency of the Tikhonov's regularization in an ill-posed problem with random data," Statistics & Probability Letters, Elsevier, vol. 79(6), pages 722-727, March.
    2. Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
    3. Chen, Xia, 1997. "Moderate deviations for m-dependent random variables with Banach space values," Statistics & Probability Letters, Elsevier, vol. 35(2), pages 123-134, September.
    4. Taisuke Otsu, 2011. "Moderate Deviations of Generalized Method of Moments and Empirical Likelihood Estimators," Cowles Foundation Discussion Papers 1785, Cowles Foundation for Research in Economics, Yale University.
    5. Jan Mielniczuk & Małgorzata Wojtyś, 2010. "Estimation of Fisher information using model selection," Metrika, Springer, vol. 72(2), pages 163-187, September.
    6. Cattiaux, Patrick & Gozlan, Nathael, 2007. "Deviations bounds and conditional principles for thin sets," Stochastic Processes and their Applications, Elsevier, vol. 117(2), pages 221-250, February.
    7. Cuevas, Antonio & Febrero, Manuel & Fraiman, Ricardo, 2006. "On the use of the bootstrap for estimating functions with functional data," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1063-1074, November.

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