Large and Moderate Deviations for Matching Problems and Empirical Discrepancies

A. Ganesh, N. O'Connell

2007, v.13, №1, 85-98

ABSTRACT

We study the two-sample matching problem and its connections with the Monge - Kantorovich problem of optimal transportation of mass. We exploit this connection to obtain moderate and large deviation principles. For the classical problem on the unit square we present a conjecture which, if true, yields an explicit formula for the rate function.

Keywords: matching problems,empirical processes,empirical discrepancies,large deviations,marriage lemma,Monge - Kantorovich problem

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