StatiStical teStS and eStimatorS of the rank of a matrix and their aPPlicationS in econometric modelling

In 2008 all ECB publications feature a motif taken from the €10 banknote. 1 We would like to thank Lucrezia Reichlin for her comments on an earlier draft. Any errors are the authors own. Fax +49 69 1344 6000 All rights reserved. Any reproduction, publication and reprint in the form of a different publication, whether printed or produced electronically, in whole or in part, is permitted only with the explicit written authorisation of the ECB or the author(s). The views expressed in this paper do not necessarily refl ect those of the European Central Bank. Abstract 4 Non-technical summary 5 1 Introduction 6 2 Rank of a general matrix 7 2.1 A minimum discrepancy function test 10 3 Rank of a hermitian positive semidefi nite matrix 12 4 Methods to identify the true rank 13 4.1 Sequential testing methods 13 4.2 Information criteria methods 14 5 Applications of tests of rank 15 5.