Suppose X1,...,Xn are i.i.d. N(, 1). Consider Hodges superefficient estimator of (unpublished, but cited in Le

Suppose X1,...,Xn are i.i.d. N(θ, 1). Consider Hodges’ superefficient estimator of θ (unpublished, but cited in Le Cam (1953)), defined as follows Let ˆθn be 0 if |X¯n| ≤ n−1/4; otherwise, let ˆθn = X¯n. For any fixed θ, determine the limiting distribution of n1/2(ˆθn − θ). Next, determine the limiting distribution of n1/2(ˆθn − θn) under θn = hn−1/2.