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Large deviations for quasi-arithmetically self-normalized random variables

Jean-Marie AubryMarguerite Zani — 2013

ESAIM: Probability and Statistics

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 on self-normalized statistics that was obtained in the homogeneous case by [Q.-M. Shao, Self-normalized large deviations. 25 (1997) 285–328]. Furthermore, in the homogenous case, we derive the Bahadur exact slope for tests using self-normalized statistics.

Diametral dimension of some pseudoconvex multiscale spaces

Jean-Marie AubryFrançoise Bastin — 2010

Studia Mathematica

Stemming from the study of signals via wavelet coefficients, the spaces S ν are complete metrizable and separable topological vector spaces, parametrized by a function ν, whose elements are sequences indexed by a binary tree. Several papers were devoted to their basic topology; recently it was also shown that depending on ν, S ν may be locally convex, locally p-convex for some p > 0, or not at all, but under a minor condition these spaces are always pseudoconvex. We deal with some more sophisticated...

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