Maximum Covariance Difference Test for Equality of Two Covariance Matrices
نویسندگان
چکیده
We propose a test of equality of two covariance matrices based on the maximum standardized difference of scalar covariances of two sample covariance matrices. We derive the tail probability of the asymptotic null distribution of the test statistic by the tube method. However the usual formal tube formula has to be suitably modified, because in this case the index set, around which the tube is formed, has zero critical radius.
منابع مشابه
On Selecting Tests for Equality of Two Normal Mean Vectors.
The conventional approach for testing the equality of two normal mean vectors is to test first the equality of covariance matrices, and if the equality assumption is tenable, then use the two-sample Hotelling T (2) test. Otherwise one can use one of the approximate tests for the multivariate Behrens-Fisher problem. In this article, we study the properties of the Hotelling T (2) test, the conven...
متن کاملTwo Sample Tests for High - Dimensional Covariance Matrices
We propose two tests for the equality of covariance matrices between two high-dimensional populations. One test is on the whole variance–covariance matrices, and the other is on off-diagonal sub-matrices, which define the covariance between two nonoverlapping segments of the high-dimensional random vectors. The tests are applicable (i) when the data dimension is much larger than the sample size...
متن کاملTests of some hypotheses on characteristic roots of covariance matrices not requiring normality assumptions
Test statistics for testing some hypotheses on characteristic roots of covariance matrices are presented, their asymptotic distribution is derived and a confidence interval for the proportional sum of the characteristic roots is constructed. The resulting procedures are robust against violation of the normality assumptions in the sense that they asymptotically possess chosen significance level ...
متن کاملError bounds for high–dimensional Edgeworth expansions for some tests on covariance matrices
Problems of testing three hypotheses : (i) equality of covariance matrices of several multivariate normal populations, (ii) sphericity, and (iii) that a covariance matrix is equal to a specified one, are treated. High–dimensional Edgeworth expansions of the null distributions of the modified likelihood ratio test statistics are derived. Computable error bounds of the expansions are derived for ...
متن کاملA Two Sample Test for Mean Vectors with Unequal Covariance Matrices
In this paper, we consider testing the equality of two mean vectors with unequal covariance matrices. In the case of equal covariance matrices, we can use Hotelling’s T 2 statistic, which follows the F distribution under the null hypothesis. Meanwhile, in the case of unequal covariance matrices, the T 2 type test statistic does not follow the F distribution, and it is also difficult to derive t...
متن کامل