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Large Deviations for Quasi-Arithmetically Self-Normalized Random Variables

Abstract : We introduce a family of convex (concave) functions called sup (inf) of powers, which are used as generator functions for a special type of quasi-arithmetic means. Using these means we generalize the large deviation result that was obtained in the homogeneous case by Shao [14] on self- normalized statistics. Furthermore, in the homogenous case, we derive the Bahadur exact slope for tests using self-normalized statistics.
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Submitted on : Monday, March 4, 2013 - 2:19:46 PM
Last modification on : Saturday, January 15, 2022 - 4:02:14 AM
Long-term archiving on: : Wednesday, June 5, 2013 - 3:55:55 AM


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Jean-Marie Aubry, Marguerite Zani. Large Deviations for Quasi-Arithmetically Self-Normalized Random Variables. ESAIM: Probability and Statistics, EDP Sciences, 2013, 17 (1), pp.1--12. ⟨hal-00796315⟩



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