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...

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...

We provide easy to verify sufficient conditions for the consistency and asymptotic normality of a class of semiparametric optimization estimators where the criterion function does not obey standard smoothness conditions and simultaneously depends on some nonparametric estimators that can...

Let (<b>"X"</b>_<b>"i"</b>,<b>"Y"</b>_<b>"i"</b>) (<b>"i"</b>&equals;<b>"1"</b>,…,<b>"n"</b>) be "n" replications of a random vector (<b>"X"</b>,<b>"Y"</b> ), where "Y" is supposed to be subject to random right censoring. The data (<b>"X"</b>_<b>"i"</b>,<b>"Y"</b>_<b>"i"</b>) are assumed to come from a stationary "&agr;"-mixing process. We consider the problem of estimating the function...

We consider the functional non-parametric regression model "Y"&equals; "r"(<b>"χ"</b>)&plus;"&epsiv;", where the response "Y" is univariate, <b>"χ"</b> is a functional covariate (i.e. valued in some infinite-dimensional space), and the error "&epsiv;" satisfies "E"("&epsiv;" | <b>"χ"</b>) &equals; 0. For this model, the pointwise...

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...