Empirical and sequential empirical copula processes play a central role for statistical inference on copulas. However, as pointed out by Johan Segers [J. Segers, Asymptotics of empirical copula processes under non-restrictive smoothness assumptions, Bernoulli 18 (3) (2012) 764–782] the usual...

An asymptotic distribution theory is developed for a general class of signed-rank serial statistics, and is then used to derive asymptotically locally optimal tests (in the maximin sense) for testing an ARMA model against other ARMA models. Special cases yield Fisher-Yates, van der Waerden, and...

A class of linear serial multirank statistics is introduced for the problem of testing the null hypothesis that a multivariate series of observations is white noise (with unspecified density function) against alternatives of ARMA dependence. The asymptotic distributional properties of these...

We develop optimal rank-based procedures for testing affine-invariant linear hypotheses on the parameters of a multivariate general linear model with elliptical VARMA errors. We propose a class of optimal procedures that are based either on residual (pseudo-)Mahalanobis signs and ranks, or on...

The purpose of this paper is to investigate kernel density estimators for spatial processes with linear or nonlinear structures. Sufficient conditions for such estimators to converge in L1 are obtained under extremely general, verifiable conditions. The results hold for mixing as well as for...

Conditions for mixed autoregressive-moving average processes with time-dependent coefficients to be purely nondeterministic and invertible can be obtained from classical difference equations theory. These conditions involve one-sided Green's functions or their matricial equivalents. A recursive...

The assumption of homogeneity of covariance matrices is the fundamental prerequisite of a number of classical procedures in multivariate analysis. Despite its importance and long history, however, this problem so far has not been completely settled beyond the traditional and highly unrealistic...

In a nonparametric regression model with a multivariate explanatory variable we consider the problem of testing the hypothesis that specific interactions in a canonical decomposition of the model vanish. A simple consistent test is developed which is based on the difference between the...

In this paper we consider random block matrices which generalize the classical Laguerre ensemble and the Jacobi ensemble. We show that the random eigenvalues of the matrices can be uniformly approximated by the zeros of matrix orthogonal polynomials and obtain a rate for the maximum difference...

In the functional regression model where the responses are curves, new tests for the functional form of the regression and the variance function are proposed, which are based on a stochastic process estimating L2-distances. Our approach avoids the explicit estimation of the functional regression...