ABSTRACT

The elements ? , ? *, ?, ?* make the parameter space T. The correspondence between this designation of the parameter point and the one in terms of (S, S11, d, d1) is given by

The element (? , ? *, 0, 0) constitute T0. Finally (as in Stein (1956)) the function P is given by

with

Now writing in terms of the elements of ? the acceptance region of Hotelling’s T2 test based on ?, ?1,…, ?n is given by

where the constant k depends on the size a of the test. Theorem 8.10.1. For testing H0: d=0 against H1: d?0, Hotelling’s T

2 test with the the acceptance region (8.252) is admissible.