Small Area Estimation Based On ADM Method Via Nested Error Regression Model

In small area estimation,commonly used variance estimation methods may produce either zero or negative estimates of the variance.This will cause problems for empirical best linear unbiased prediction(EBLUP)and its statistical inference for small area means.In this paper,we extend the Adjustment for Density Maximization method(ADM)to the nested error regression model with two unknown variance components under the EBLUP method,and study the EBLUP and its mean square prediction error(MSPE)of small area mean.The numerical simulation results in this paper show that the adjusted maximum likelihood method(ADM ML)and the adjusted restricted maximum likelihood method(ADM REML)based on the ADM method can obtain a strictly positive uniform estimate of the variance of the random effects,and this correction does not affect the MSPE of the variance estimator and the EBLUP estimate of the small area mean.In addition,the ADM ML estimate is superior to the ADM REML estimate in terms of bias.This can solve the problems related to the EBLUP estimation and its MSPE estimation of small area mean caused by the zero estimation of variance in the nested error regression model.