Cramér’s Theorem is Atypical

@article{Gantert2016CramrsTI,
  title={Cram{\'e}r’s Theorem is Atypical},
  author={N. Gantert and S. S. Kim and K. Ramanan},
  journal={arXiv: Probability},
  year={2016},
  pages={253-270}
}
  • N. Gantert, S. S. Kim, K. Ramanan
  • Published 2016
  • Mathematics
  • arXiv: Probability
  • The empirical mean of n independent and identically distributed (i.i.d.) random variables \((X_1,\dots ,X_n)\) can be viewed as a suitably normalized scalar projection of the n-dimensional random vector \(X^{(n)}\displaystyle \mathop {=}^{\cdot }\,(X_1,\dots ,X_n)\) in the direction of the unit vector \(n^{-1/2}(1,1,\dots ,1) \in \mathbb {S}^{n-1}\). The large deviation principle (LDP) for such projections as \(n\rightarrow \infty \) is given by the classical Cramer’s theorem. We prove an LDP… CONTINUE READING
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