In this article, we propose a new test for additivity in nonparametric quan-tile regression with a high-dimensional predictor. Asymptotic normality of the corresponding test statistic (after appropriate standardization) is established under the null hypothesis, local and fixed alternatives. We also propose a bootstrap procedure which can be used to improve… (More)
In this paper we define distributions on the moment spaces corresponding to p × p real or complex matrix measures on the real line with an unbounded support. For random vectors on the unbounded matricial moment spaces we prove the convergence in distribution to the Gaussian orthogonal ensemble or the Gaussian unitary ensemble, respectively.
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 roots of matrix orthogonal polynomials and obtain a rate for the maximum difference between the eigenvalues and the roots. This relation between the… (More)