Worst-case large deviations upper bounds for i.i.d. sequences under ambiguity
Author(s)
Date
2018Source Title
Turkish Journal of Mathematics
Print ISSN
1300-0098
Electronic ISSN
1303-6149
Publisher
TÜBİTAK
Volume
42
Pages
257 - 271
Language
English
Type
ArticleItem Usage Stats
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Abstract
An introductory study of large deviations upper bounds from a worst-case perspective under parameter
uncertainty (referred to as ambiguity) of the underlying distributions is given. Borrowing ideas from robust optimization, suitable sets of ambiguity are defined for imprecise parameters of underlying distributions. Both univariate and
multivariate i.i.d. sequences of random variables are considered. The resulting optimization problems are challenging
min–max (or max–min) problems that admit some simplifications and some explicit results, mostly in the case of the
normal probability law.
Keywords
Large deviationsAmbiguity
Robust optimization
Ellipsoids
Legendre–Fenchel transform
Min–max theorem