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A Note on the Bias of O'Brien's OLS Test
Author(s) -
Frick Hans
Publication year - 1997
Publication title -
biometrical journal
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.108
H-Index - 63
eISSN - 1521-4036
pISSN - 0323-3847
DOI - 10.1002/bimj.4710390112
Subject(s) - mathematics , ordinary least squares , covariance matrix , statistics , test (biology) , covariance , matrix (chemical analysis) , estimation of covariance matrices , wald test , multivariate statistics , statistical hypothesis testing , econometrics , paleontology , biology , materials science , composite material
O'Brien's Ordinary Least Squares (OLS) test is a well known procedure for testing the multivariate one‐sided hypothesis when the covariance matrix is unknown. Simulation results have been reported where the actual test level exceeds the nominal one. Here it is shown analytically that the actual level is always larger than the nominal one if the covariance matrix is nonnegative.