We suggest a new consistent asymptotically distribution-free test for independence of the components of bivariate random variables. The approach combines methods of order-selection tests with nonparametric copula density estimation. We deduce the asymptotic distribution of the test statistic and...

We propose a new test for independence of error and covariate in a nonparametric regression model. The test statistic is based on a kernel estimator for the L2-distance between the conditional distribution and the unconditional distribution of the covariates. In contrast to tests so far...

The objective of this paper is to estimate a bivariate density nonparametrically from a dataset from the joint distribution and datasets from one or both marginal distributions. We develop a copula-based solution, which has potential benefits even when the marginal datasets are empty. For...

In this paper we consider the estimation of the error distribution in a heteroscedastic nonparametric regression model with multivariate covariates. As estimator we consider the empirical distribution function of residuals, which are obtained from multivariate local polynomial fits of the...

Recently, Dette et al. [A simple nonparametric estimator of a strictly increasing regression function. Bernoulli 12, 469-490] proposed a new monotone estimator for strictly increasing nonparametric regression functions and proved asymptotic normality. We explain two modifications of their method...

In this paper collections of two-sample U-statistics are considered as a U-process indexed by a class of kernels. Sufficient conditions for a functional central limit theorem in the non-degenerate case are given and a uniform law of large numbers is obtained. The conditions are in terms of...