Hotelling's T2Test Under Symmetry Conditions

The familiar Hotelling's T 2 statistic used for testing the null hypothesis that a collection of observed vectors has mean vector 0 is discussed outside the usual framework of independently and identically distributed multivariate normal observations. A wider null hypothesis called “orthant symmetry” is introduced, and certain robustness properties of the T 2 statistic within this null hypothesis are demonstrated. (In particular, orthant symmetry includes the case where the vectors are generated independently and normally with mean vector 0, but each with a different covariance matrix.) Relationships of T 2 with various rank statistic tests are discussed.