Large deviations for weighted empirical mean with outliers

M. Maïda, J. Najim and S. Péché

Stochastic Processes and their Applications, 2007, vol. 117, issue 10, 1373-1403

Abstract: We study in this article the large deviations for the weighted empirical mean , where is a sequence of -valued independent and identically distributed random variables with some exponential moments and where the deterministic weights are mxd matrices. Here is a continuous application defined on a locally compact metric space and we assume that the empirical measure weakly converges to some probability distribution R with compact support . The scope of this paper is to study the effect on the Large Deviation Principle (LDP) of outliers, that is elements such that We show that outliers can have a dramatic impact on the rate function driving the LDP for Ln. We also show that the statement of a LDP in this case requires specific assumptions related to the large deviations of the single random variable . This is the main input with respect to a previous work by Najim [J. Najim, A Cramér type theorem for weighted random variables, Electron. J. Probab. 7 (4) (2002) 32 (electronic)].

Keywords: Large; deviations; Spherical; integrals; Spiked; models (search for similar items in EconPapers)
Date: 2007
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Citations: View citations in EconPapers (1)

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