ON THE ASYMPTOTIC PROPERTIES OF LDU-BASED TESTS OF THE RANK OF A MATRIX

Gill and Lewbel recently introduced a test for the rank of a matrix ba sed on the LDU decomposition. Unfortunately, the asymptotic distributi on suggested by them is incorrect except in a very limited problem. In general, the asymptotic distribution is that of a highly complicated nonlinear function of a normally distributed random vector that appear s to defy useful characterization. The LDU decomposition can be used t o produce a valid test asymptotically equivalent to the minimum-chi(2) test.