A HIGH DIMENSIONAL TWO SAMPLE SIGNIFICANCE TEST

摘要: 0. Summary. The classical multivariate 2 sample significance test based on Hotelling's T2 is undefined when the number k of variables exceeds within degrees freedom available for estimation variances and covariances. Addition an a priori Euclidean metric to affine k-space assumed by method leads alternative approach same problem. A statistic F which ratio mean square distances proposed 3 methods attaching level are described. third considered in detail "non-exact" where null hypothesis distribution depends, approximation, single unknown parameter r estimate must be substituted. Approximate theory independent estimates nearly sufficient statistics these may combined yield estimate. nominally at 5 % but rather than itself has true function r. This investigated shown quite near %. sensitivity measuring statistical distance between population means discussed it that arbitrarily small differences each individual variable can result detectable overall difference provided (or, more precisely, r) made sufficiently large. discussion stated implications choice k-space. Finally geometrical description case large presented. 1. Introduction. problem here treated testing k-variate populations have structure covariances, being from with sizes denoted ni n2 . It intended provide applicable data characteristics measured individuals small. usual encounters mathematical barrier becomes inapplicable > + - 2, certainly need arisen applied work techniques handling samples highly described individuals. equivalent formulations terms