|
|
Article: On the asymptotic properties of LDU-based tests of the rank of a matrix.
- Article from:
- Journal of the American Statistical Association
- Article date:
- September 1, 1996
- Author:
CopyrightCOPYRIGHT 1996 American Statistical Association. This material is published under license from the publisher through the Gale Group, Farmington Hills, Michigan. All inquiries regarding rights should be directed to the Gale Group. (Hide copyright information)
|
Gill and Lewbel recently introduced a test for the rank of a matrix based on the LDU decomposition. Unfortunately, the asymptotic distribution 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 appears to defy useful characterization. The LDU decomposition can be used to produce a valid test asymptotically equivalent to the minimum-[X.sup.2] test.
KEY WORDS: Estimated matrices; Gaussian elimination, Minimum [X.sup.2].
1. INTRODUCTION
In an important paper, Gill and Lewbel (1992), hereafter ...