A Statistical Test for the Stability of Covariance Structure

The stability of covariance matrix is a major issue in multivariate analysis. As can be seen in the literature, the most popular and widely used tests are Box M-test and Jennrich J-test introduced by Box in 1949 and Jennrich in 1970, respectively. These tests involve determinant of sample covariance matrix as multivariate dispersion measure. Since it is only a scalar representation of a complex structure, it cannot represent the whole structure. On the other hand, they are quite cumbersome to compute when the data sets are of high dimension since they do not only involve the computation of determinant of covariance matrix but also the inversion of a matrix. This motivates us to propose a new statistical test which is computationally more efficient and, if it is used simultaneously with M-test or J-test, we will have a better understanding about the stability of covariance structure. An example will be presented to illustrate its advantage.