Uniform confidence bands for densities f via nonparametric kernel estimates were first constructed by Bickel and Rosenblatt [Ann. Statist. 1, 1071.1095]. In this paper this is extended to confidence bands in the deconvolution problem g = f for an ordinary smooth error density . Under certain...

In this paper we investigate several tests for the hypothesis of a parametric form of the error distribution in the common linear and nonparametric regression model, which are based on empirical processes of residuals. It is well known that tests in this context are not asymptotically...

The aim of this paper is to show that existing estimators for the error distribution in nonparametric regression models can be improved when additional information about the distribution is included by the empirical likelihood method. The weak convergence of the resulting new estimator to a...

In the classical linear regression model the problem of testing for symmetry of the error distribution is considered. The test statistic is a functional of the difference between the two empirical distribution functions of the estimated residuals and their counterparts with opposite signs. The...

The purpose of this paper is to propose a procedure for testing the equality of several regression curves fi in nonparametric regression models when the noise is inhomogeneous. This extends work of Dette and Neumeyer (2001) and it is shown that the new test is asymptotically uniformly more...

During the past the convergence analysis for linear statistical inverse problems has mainly focused on spectral cut-off and Tikhonov type estimators. Spectral cut-off estimators achieve minimax rates for a broad range of smoothness classes and operators, but their practical usefulness is limited...

The computation of robust regression estimates often relies on minimization of a convex functional on a convex set. In this paper we discuss a general technique for a large class of convex functionals to compute the minimizers iteratively which is closely related to majorization-minimization...

In the common nonparametric regression model y(i) = g(ti) + a (ti) ei , i=1….,n with i.i.d - noise and nonrepeatable design points ti we consider the problem of choosing an optimal design for the estimation of the regression function g. A minimax approach is adopted which searches for designs...