Nestor Parolya: Testing for Independence of Large Dimensional Vectors
Tid: On 2017-05-03 kl 15.15 - 16.15
Plats: Room 306, House 6, Kräftriket, Department of Mathematics, Stockholm University
Medverkande: Nestor Parolya (University of Hannover)
Abstract: In this paper new tests for the independence of two high dimensional vectors are investigated. We consider the case where the dimension of the vectors increases with the sample size and propose multivariate analysis of variance-type statistics for the hypothesis of a block diagonal covariance matrix. The asymptotic properties of the new test statistics are studied under the null hypothesis and the alternative using random matrix theory. For this purpose we study the asymptotic properties of linear spectral statistics of central and non-central Fisher matrices.
In particular we derive a central limit theorem for linear spectral statistics of large dimension non-central Fisher matrices, which can be used to analyse the power of the tests under the alternative. The theoretical results are illustrated by means of a simulation study, where we also compare the new tests with the commonly used likelihood ratio test. In particular it is demonstrated that the latter test does not keep its nominal level, if the dimension of one vector is relatively small compared to the dimension of the other vector. On the other hand the tests proposed in this paper provide a reasonable approximation of the nominal level in such situations.