## Journal of Applied Probability

### Sample path large deviations for order statistics

#### Abstract

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

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

Dates
First available in Project Euclid: 15 March 2011

https://projecteuclid.org/euclid.jap/1300198147

Digital Object Identifier
doi:10.1239/jap/1300198147

Mathematical Reviews number (MathSciNet)
MR2809898

Zentralblatt MATH identifier
1229.62058

#### Citation

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. https://projecteuclid.org/euclid.jap/1300198147

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