Multidimensional strong large deviation results

Cyrille Joutard ()
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Cyrille Joutard: Université Paul-Valéry Montpellier 3

Metrika: International Journal for Theoretical and Applied Statistics, 2017, vol. 80, issue 6, No 4, 663-683

Abstract: 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.

Keywords: Large deviations; Bahadur–Rao theorem; Sample variances; Gaussian multiple linear regression model; Multivariate Nadaraya–Watson estimator (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s00184-017-0621-4

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