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

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.

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Year of publication:	2012
Authors:	Yang, Xiangfeng
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 82.2012, 2, p. 291-294
Publisher:	Elsevier
Subject:	Cramér’s Theorem \| Empirical means \| Rate function

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10011040052