Empirical processes for non ergodic data are investigated under uniform distance. Some CLTs, both uniform and non uniform, are proved. In particular, conditions for Bn = n^(1/2) (µn - bn) and Cn = n^(1/2) (µn - an) to converge in distribution are given, where µn is the empirical measure, an...

Empirical processes for non ergodic data are investigated under uniform distance. Some CLTs, both uniform and non uniform, are proved. In particular, conditions for Bn = n^(1/2) (µn - bn) and Cn = n^(1/2) (µn - an) to converge in distribution are given, where µn is the empirical measure, an...

We show that the empirical process of the squared residuals of an ARCH(p) sequence converges in distribution 1,0 a Gaussirm process B(F(t)) +t f(t) e, where F is the distribution function of the squared innovations, f its derivative, {B(tl, 0 <; t>1} a Brownian bridge and e a normal random variable.

In this paper a new test for the parametric form of the variance function in the common nonparametric regression model is proposed which is applicable under very weak assumptions. The new test is based on an empirical process formed from pseudo residuals, for which weak convergence to a Gaussian...

In this paper a new test for the parametric form of the variance function in the common nonparametric regression model is proposed which is applicable under very weak smoothness assumptions. The new test is based on an empirical process formed from pseudo residuals, for which weak convergence to...

Almost sure convergence for ratios of delta functions establishes global and local strong consistency for a variety of estimates and data generations. For instance, the empirical probability function from independent identically distributed random vectors, the empirical distribution for...

In this paper, we propose a model-free bootstrap method for the empirical process under absolute regularity. More precisely, consistency of an adapted version of the so-called dependent wild bootstrap, that was introduced by Shao (2010) and is very easy to implement, is proved under minimal...

We derive strong approximations to the supremum of the non-centered empirical process indexed by a possibly unbounded VC-type class of functions by the suprema of the Gaussian and bootstrap processes. The bounds of these approximations are non-asymptotic, which allows us to work with classes of...

This paper develops a new direct approach to approximating suprema of general empirical processes by a sequence of suprema of Gaussian processes, without taking the route of approximating whole empirical processes in the sup-norm. We prove an abstract approximation theorem applicable to a wide...

We analyze the properties of non- and semiparametric estimation procedures involving nonparametric regression with generated covariates. Such estimators appear in numerous econometric applications, including nonparametric estimation of simultaneous equation models, sample selection models,...