EMPIRICAL BEST PREDICTION FOR SMALL AREA INFERENCE WITH BINARY DATA

JIMING JIANG^{1} AND P. LAHIRI^{2}

1Department of Statistics, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, OH 44106-7054, U.S.A. 2Department of Mathematics and Statistics, University of Nebraska at Lincoln, Lincoln, NE 68588-0323, U.S.A.

(Received December 9, 1998; revised September 27, 1999)

Abstract. The paper introduces a frequentist’s alternative to the recently developed hierarchical Bayes methods for small area estimation with binary data. Specifically, the best predictor (BP) and empirical best predictor (EBP) of small area specific random effect are developed in the context of a mixed logistic model and different asymptotic properties of the proposed BP and EBP are studied. An approximation to the mean squared error (MSE) of the proposed EBP correct up to the order o(m^{−1}) is obtained, where m denotes the number of small areas. The asymptotic behavior of the relative savings loss (RSL) demonstrates the superiority of the proposed EBP over the usual small area proportion.

Key words and phrases: Asymptotics, composite estimation, empirical best predictor, Laplace approximation, method of moments, mixed models, MSE.