2.13 Let bn() = E (n) be the bias of the estimator n of Example...

2.13 Let bn(θ) = Eθ (δn) − θ be the bias of the estimator δn of Example 2.5.

(a) Show that bn(θ) = −(1 − a)

√n

 √4 n

−√4 n xφ(x − √nθ) dx;

(b) Show that b

n(θ) → 0 for any θ = 0 and b

n(0) → (1 − a).

(c) Use

(b) to explain how the Hodges estimator δn can violate (2.7) without violating the information inequality.