An elementary proof of the lower bound of Cramér’s Theorem in Rd

Xiangfeng Yang

Statistics & Probability Letters, 2012, vol. 82, issue 2, 291-294

Abstract: Let {ξi} be a family of i.i.d. random vectors in Rd(d≥2), and μn be the distributions in Rd of the empirical means ξ1+⋯+ξnn. Without imposing any conditions, a new and elementary approach is presented in this note for showing the lower bound of the large deviation principle for {μn}, lim infn→∞1nlnμn(O)≥−infx∈OΛ⋆(x),open O⊆Rd, for some rate function Λ⋆(⋅) which is defined in this note.

Keywords: Cramér’s Theorem; Empirical means; Rate function (search for similar items in EconPapers)
Date: 2012
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DOI: 10.1016/j.spl.2011.10.007

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