Asymptotic expansions of some test criteria for homogeneity of variances and covariance matrices from normal populations

154 1. Preliminaries 2. Asymptotic expansions of Lehmann's test under local alternatives 3. Asymptotic expansions of Bartlett's test under local alternatives 4. Numerical examples PART II.SPHERICITY TEST 188 5. Asymptotic expansions under local alternatives 6