1、Testing the rank and definiteness of estimated matrices with applications to factor, state-space and arma models
Gill  and Lewbel
Journal of the American Statistical Association
http://www.jstor.org/pss/2290214

2、Inferring the rank of a matrix
John G. Cragg and Stephen G. Donald
Journal of Econometrics
Volume 76, Issues 1-2, January-February 1997, Pages 223-250
http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6VC0-3T7HKRP-C&_user=10&_coverDate=02%2F28%2F1997&_rdoc=1&_fmt=high&_orig=search&_origin=search&_sort=d&_docanchor=&view=c&_searchStrId=1536855915&_rerunOrigin=scholar.google&_acct=C000050221&_version=1&_urlVersion=0&_userid=10&md5=dcd9793fab54ee93e0ac74073e609056&searchtype=a