Sample path large deviations for order statistics

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