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Exponential inequalities for sums of random vectors


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  • Yurinskii, V. V.
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    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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    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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    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. 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.
    2. Jan Mielniczuk & Małgorzata Wojtyś, 2010. "Estimation of Fisher information using model selection," Metrika, Springer, vol. 72(2), pages 163-187, September.
    3. Cardot, Hervé & Sarda, Pacal, 2005. "Estimation in generalized linear models for functional data via penalized likelihood," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 24-41, January.
    4. Cardot, Hervé & Ferraty, Frédéric & Sarda, Pascal, 1999. "Functional linear model," Statistics & Probability Letters, Elsevier, vol. 45(1), pages 11-22, October.
    5. 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.
    6. Boente, Graciela & Fraiman, Ricardo, 2000. "Kernel-based functional principal components," Statistics & Probability Letters, Elsevier, vol. 48(4), pages 335-345, July.
    7. 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.
    8. 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.
    9. 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.


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