Given an observation of the uniform empirical process [alpha]n, its functional increments [alpha]n(u+an[dot operator])-[alpha]n(u) can be viewed as a single random process, when u is distributed under the Lebesgue measure. We investigate the almost sure limit behaviour of the multivariate...

Let (Xi)i=1 be an i.i.d. sample on having density f. Given a real function [phi] on with finite variation, and given an integer valued sequence (jn), let denote the estimator of f by wavelet projection based on [phi] and with multiresolution level equal to jn. We provide exact rates of almost...

Suppose that "X"_<b>1</b>,…, "X"_<b>""n""</b> is a sequence of independent random vectors, identically distributed as a "d"-dimensional random vector "X". Let <formula format="inline"><file name="sjos_640_mu1.gif" type="gif" /></formula> be a parameter of interest and <formula format="inline"><file name="sjos_640_mu2.gif" type="gif" /></formula> be some nuisance parameter. The unknown, true parameters ("μ"_<b>0</b>,"ν"_<b>0</b>) are uniquely determined by the system of...

Several testing procedures are proposed that can detect change-points in the error distribution of non-parametric regression models. Different settings are considered where the change-point either occurs at some time point or at some value of the covariate. Fixed as well as random covariates are...

Several classical time series models can be written as a regression model between the components of a strictly stationary bivariate process. Some of those models, such as the ARCH models, share the property of proportionality of the regression function and the scale function, which is an...

In the common non-parametric regression model the problem of testing for the parametric form of the conditional variance is considered. A stochastic process based on the difference between the empirical processes that are obtained from the standardized non-parametric residuals under the null...