Empirical Discrepancies and Subadditive Processes

Empirical Phi-discrepancies and Quasi-empirical Likelihood: Exponential Bounds

We review some recent extensions of the so-called generalized empirical likelihood method, when the Kullback distance is replaced by some general convex divergence. We propose to use, instead of empirical likelihood, some regularized form or quasi-empirical likelihood method, corresponding to a convex combination of Kullback and χ2 discrepancies. We show that for some adequate choice of the wei...

Kingman's Subadditive Ergodic Theorem Kingman's Subadditive Ergodic Theorem

A simple proof of Kingman’s subadditive ergodic theorem is developed from a point of view which is conceptually algorithmic and which does not rely on either a maximal inequality or a combinatorial Riesz lemma.

Large and moderate deviations for matching problems and empirical discrepancies

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.

Subadditive Ergodic Theorems

Above is the famous Fekete’s lemma which demonstrates that the ratio of subadditive sequence (an) to n tends to a limit as n approaches infinity. This lemma is quite crucial in the field of subadditive ergodic theorems because it gives mathematicians some general ideas and guidelines in the non-random setting and leads to analogous discovery in the random setting. Kingman’s Subadditive Ergodic ...

EMPIRICAL PROCESSES: Theory and Applications