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Multidimensional strong large deviation results

Author

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  • Cyrille Joutard

    (Université Paul-Valéry Montpellier 3
    CNRS, Institut Montpelliérain Alexander Grothendieck, Univ. Montpellier)

Abstract

We establish strong large deviation results for an arbitrary sequence of random vectors under some assumptions on the normalized cumulant generating function. In other words, we give asymptotic approximations for a multivariate tail probability of the same kind as the one obtained by Bahadur and Rao (Ann Math Stat 31:1015–1027, 1960) for the sample mean (in the one-dimensional case). The proof of our results follows the same lines as in Chaganty and Sethuraman (J Stat Plan Inference, 55:265–280, 1996). We also present three statistical applications to illustrate our results, the first one dealing with a vector of independent sample variances, the second one with a Gaussian multiple linear regression model and the third one with the multivariate Nadaraya–Watson estimator. Some numerical results are also presented for the first two applications.

Suggested Citation

  • Cyrille Joutard, 2017. "Multidimensional strong large deviation results," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 80(6), pages 663-683, November.
    • Handle: RePEc:spr:metrik:v:80:y:2017:i:6:d:10.1007_s00184-017-0621-4
    DOI: 10.1007/s00184-017-0621-4
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    References listed on IDEAS

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    1. Cyrille Joutard, 2013. "Strong large deviations for arbitrary sequences of random variables," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(1), pages 49-67, February.
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    Cited by:

    1. Hui Jiang & Jin Shao & Qingshan Yang, 2021. "Sharp large deviations for a class of normalized L-statistics and applications," Statistical Papers, Springer, vol. 62(2), pages 721-744, April.

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