On some properties of hammersley's estimator of an integer mean

Let X1, ., Xn be i.i.d.N(i, 1), i = 0, ± 1, ± 2,..Hammersley [2] proposed [X.n], the nearest integer to the sample mean, as an estimator of i.It is proved that d is minimax and admissible relative to zero-one loss.However, it is shown that relative to squared error loss, the estimator is neither admissible nor minimax.