Miguel A. Arcones

Central limit theorems for empirical andU-processes of stationary mixing sequences

AbstractThis paper gives sufficient conditions for the weak convergence to Gaussian processes of empirical processes andU-processes from stationary β mixing sequences indexed byV-C subgraph classes of functions. If the envelope function of theV-C subgraph class is inLp for some 2<p<∞, we obtain a uniform central limit theorem for the empirical process under the β mixing condition

The Large Deviation Principle for Stochastic Processes. II

k^{p/(p - 2)} (\log k)^{2(p - 1)/(p - 2)} \beta _k \to 0 as k \to \infty

On the law of the iterated logarithm for canonical U-statistics and processes

In the case that the functions in theV-C subgraph class are uniformly bounded, we obtain uniform central limit theorems for the empirical process and theU-process, provided that the decay rate of the β mixing coefficient satisfies βk=O(k−r) for somer>1. These conditions are almost minimal.

Nonparametric Estimation of a Distribution Subject to a Stochastic Precedence Constraint

Some important aspects of chaos random variables such as decoupling, an almost sure representation (a Karhunen-Loeve expansion) and integrability are discussed here, the first being a tool for, and the third as a consequence of, the second. The main goal in this note is to learn about the structure of the limit laws ofU-processes.

A Bernstein-type inequality for U-statistics and U-processes☆

We discuss the large deviation principle of stochastic processes as random elements of~

U-processes indexed by Vapnik-Červonenkis classes of functions with applications to asymptotics and bootstrap of U-statistics with estimated parameters

l_{\infty}(T)

ASYMPTOTIC THEORY FOR M -ESTIMATORS OVER A CONVEX KERNEL

. We show that the large deviation principle in

The Bahadur-Kiefer Representation of Lp Regression Estimators

l_{\infty}(T)