3.32 For the situation of Note 9.3:

(a) Show that equivariant estimators of  are of the form cS, where S is the crossproducts matrix and c is a constant.

(b) Show that EI {tr[(cS − I )



(cS − I )]} is minimized by c = EI trS/EI trS2.

[Hint: For part (a), use a generalization of Theorem 3.3; see the argument leading to

(3.29), and Example 3.11.]