Stephane Boucheron  (joint work with Pascal Massart (Orsay))

Title: A poor man's Wilks phenomenon

Abstract:

Wilks phenomenon asserts that that in regular models,  twice the difference  between the maximum  log likelihood and the log-likelihood at the true parameter is asymptotically distributed according to a chi-square distribution with a number of degrees of freedom that coincide with the dimension of the model. We attempt to generalize this phenomenon to  other contrast minimization problems such as encountered in statistical learning theory. We provide (non-asymptotic) concentration inequalities for empirical excess risk  by combining (almost) classical tail bounds