ROBUST ESTIMATION OF MEAN SQUARED ERROR OF SMALL-AREA ESTIMATORS

A well-known model, due to Fay and Herriot, for estimating small area( domain) means, mu(i), is considered. Given mu(i)'s, it is assumed that the survey estimators, y(i), are independent with means mu(i) and kno wn variances D-i, i = l,...,t. Further, the mu(i)'s are assumed to be independent with means x'(i) beta and unknown variance. A, where x(i) is a vector of benchmark variables related to mu(i) and beta is a vect or of regression parameters, An empirical best linear unbiased predict ion (EBLUP) estimator or an empirical linear Bayes estimator, t(i) ((A ) over cap, y), of mu(i) is obtained. It is shown that an estimator of mean squared error (MSE) of t(i) ((A) over cap, y), derived by Prasad and Rao under normality of mu(i) and y(i) given mu(i), is robust with respect to nonnormality of the mu(i)'s. Specifically, it is shown tha t the Prasod-Rao estimator of MSE is correct to terms of order O(t(-1) ) for large t, assuming only certain moment conditions on the mu(i)'s and normally distributed survey errors. Results of a simulation study on the accuracy of the estimator of MSE, under nonnormality of the mu( i)'s, are also presented.