Testing Equality of Covariance Matrices via Pythagorean Means
We provide a new test for equality of covariance matrices that leads to a convenient mechanism for testing speciﬁcation using the information matrix equality. The test relies on a new characterization of equality between two k dimensional positive-deﬁnite matrices A and B : the traces of AB –1 and BA –1 are equal to k if and only if A = B . Using this criterion, we introduce a class of omnibus test statistics for equality of covariance matrices and examine their null, local, and global approximations under some mild regularity conditions. Monte Carlo experiments are conducted to explore the performance characteristics of the test criteria and provide comparisons with existing tests under the null hypothesis and local and global alternatives. The tests are applied to the classic empirical models for voting turnout investigated by Wolﬁnger and Rosenstone (1980) and Nagler (1991, 1994). Our tests show that all classic models for the 1984 presidential voting turnout are misspeciﬁed in the sense that the information matrix equality fails.
Cho, Jin Seo and Phillips, Peter C.B., "Testing Equality of Covariance Matrices via Pythagorean Means" (2014). Cowles Foundation Discussion Papers. 2384.