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Duffy, Ken R., 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: | 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: | https://mu.eprints-hosting.org/id/eprint/6220 |
| 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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