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.

MoreLess

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

Online Resource

Check full text access |

More access options

Check Google Scholar

In libraries world-wide (WorldCat)

In German libraries (KVK)

subito order

I need help

More details

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

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