Journal of Applied Probability

Sample path large deviations for order statistics

Ken R. Duffy, Claudio Macci, and Giovanni Luca Torrisi

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We consider the sample paths of the order statistics of independent and identically distributed 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 Skorokhod MM1 topology. Sanov's theorem is deduced in the Skorokhod 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.

Article information

J. Appl. Probab., Volume 48, Number 1 (2011), 238-257.

First available in Project Euclid: 15 March 2011

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Zentralblatt MATH identifier

Primary: 60F10: Large deviations 62G30: Order statistics; empirical distribution functions

Large deviation order statistic empirical law Skorokhod topology weak convergence


Duffy, Ken R.; Macci, Claudio; Torrisi, Giovanni Luca. Sample path large deviations for order statistics. J. Appl. Probab. 48 (2011), no. 1, 238--257. doi:10.1239/jap/1300198147.

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