On the Asymptotic Properties of LDU-Based Tests of the Rank of a Matrix
作者:
JohnG. Cragg,
StephenG. Donald,
期刊:
Journal of the American Statistical Association
(Taylor Available online 1996)
卷期:
Volume 91,
issue 435
页码: 1301-1309
ISSN:0162-1459
年代: 1996
DOI:10.1080/01621459.1996.10476999
出版商: Taylor & Francis Group
关键词: Estimated matrices;Gaussian elimination;MinimumX2
数据来源: Taylor
摘要:
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-X2test.
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