Empirical processes indexed by smooth functions

Empirical processes indexed by estimated functions

We consider the convergence of empirical processes indexed by functions that depend on an estimated parameter η and give several alternative conditions under which the “estimated parameter” ηn can be replaced by its natural limit η0 uniformly in some other indexing set Θ. In particular we reconsider some examples treated by Ghoudi and Remillard [Asymptotic Methods in Probability and Statistics ...

Weak convergence of empirical copula processes indexed by functions

DRAGAN RADULOVIĆ1, MARTEN WEGKAMP2 and YUE ZHAO3 1Department of Mathematics, Florida Atlantic University, 777 Glades Road, Boca Raton, FL 33431, USA. E-mail: [email protected] 2Department of Mathematics and Department of Statistical Science, Cornell University, 432 Malott Hall, Ithaca, NY 14853, USA. E-mail: [email protected] 3Department of Statistical Science, Cornell University, 310 M...

Rates of Growth and Sample Moduli for Weighted Empirical Processes Indexed by Sets

Probability inequalities are. obtained for the supremum of a weighted empirical process indexed. by a Vapnik-Cervonenkis class C of sets. These inequalities are particularly useful under the assumption P(ufC E: C : P(C) < t D -? 0 as t -? o. They are used to obtain almost sure bounds on the rate of growth of the process as the sample size approaches infinity, to find an asymptotic sample modulu...

A Kriging procedure for processes indexed by graphs

Reflection Positive Stochastic Processes Indexed by Lie Groups

Reflection positivity originates from one of the Osterwalder–Schrader axioms for constructive quantum field theory. It serves as a bridge between euclidean and relativistic quantum field theory. In mathematics, more specifically, in representation theory, it is related to the Cartan duality of symmetric Lie groups (Lie groups with an involution) and results in a transformation of a unitary repr...