Duffy, Ken R. and Macci, Claudio and Torrisi, Giovanni Luca (2011) Sample path large deviations for order statistics. Journal of Applied Probability, 48 (1). pp. 238-257. ISSN 0021-9002

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Abstract

We consider the sample paths of the order statistics of i.i.d. random variables with common distribution function F. If F is strictly increasing but possibly having discontinuities, we prove that the sample paths of the order statistics satisfy the large deviation principle in the Skorohod M₁ topology. Sanov’s Theorem is deduced in the Skorohod M'₁. topology as a corollary to this result. A number of illustrative examples are presented, including applications to the sample paths of trimmed means and Hill Plots.

Item Type:	Article
Additional Information:	This is the preprint version of the published article, which is available at doi:10.1239/jap/1300198147
Keywords:	Large deviation; order statistic; empirical law; Skorokhod topology; weak convergence;
Academic Unit:	Faculty of Science and Engineering > Research Institutes > Hamilton Institute
Item ID:	6220
Identification Number:	https://doi.org/10.1239/jap/1300198147
Depositing User:	Dr Ken Duffy
Date Deposited:	01 Jul 2015 15:25
Journal or Publication Title:	Journal of Applied Probability
Publisher:	Applied Probability Trust
Refereed:	Yes
URI:
Use Licence:	This item is available under a Creative Commons Attribution Non Commercial Share Alike Licence (CC BY-NC-SA). Details of this licence are available here

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