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    Sample path large deviations for order statistics


    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:

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