Bock (1975, TheoremA) established that for X N(, I K ) then for any scalar function g (x) E Xh X0X

Bock (1975, TheoremA) established that for X » N(µ, I K ) then for any scalar function g (x)

E

£

Xh

¡

X0X

¢¤

Æ µE[h (QKÅ2)]

where QKÅ2 » Â2 KÅ2(¸). Assume bµ » N(µ, I K ) and eµJS Æ

µ

1¡

K ¡2 bµ0bµ

¶

bµ.

(a) Use Bock’s result to calculate E

·

1 bµ0bµ

bµ

¸

. You can represent your answer using the function JK .

(b) Calculate the bias of eµJS.

(c) Describe the bias. Is the estimator biased downwards, upwards, or towards zero?