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      Worst-case large deviations upper bounds for i.i.d. sequences under ambiguity

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      Author(s)
      Pınar, Mustafa Çelebi
      Date
      2018
      Source Title
      Turkish Journal of Mathematics
      Print ISSN
      1300-0098
      Electronic ISSN
      1303-6149
      Publisher
      TÜBİTAK
      Volume
      42
      Pages
      257 - 271
      Language
      English
      Type
      Article
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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 deviations
      Ambiguity
      Robust optimization
      Ellipsoids
      Legendre–Fenchel transform
      Min–max theorem
      Permalink
      http://hdl.handle.net/11693/48519
      Published Version (Please cite this version)
      https://doi.org/10.3906/mat-1607-20
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