The mean squared prediction error (MSPE) has been used as an important measure of uncertainty in small area estimation.It is desirable to produce a second-order unbiased MSPE estimator, that is, the bias of the estimator is o(m -1 ), where m is the total number of small areas for which data are available.The task is difficult, however, especially if one needs to take into consideration that an MSPE estimator needs to be positive, or at least nonnegative.In fact, very few MSPE estimators have the property of being …