Small Area Estimation With Temporal And Estimation Of Its MSE

This article consider small area estimation under a nested error model with time effects proposed by Rao & Yu(1994).We suggest three different methods for estimating the model parameters in different cases.When the autocorrelation coefficient rho is unknown and T is small,we can directly estimate the overall parameter to avoid estimating ρ as T grows,we use the first order difference form of y to avoid estimating random effects,by which the non-convergence issue is solved.In addition,we use the Gauss Seidel algorithm proposed by Jiang(2000)to solve the problem that the estimated value of ρ often exceeds the allowable range.then we develop empirical best prediction(EBP)and empirical best linear unbiased prediction(EBLUP)of small area means.Both Jackknife and Prasad-Rao estimators of the mean squared prediction errors(MSPE)are obtained to estimate the MSPEs of the EBP and EBLUP.Theoretical and empirical studies are carried out to investigate the performance of the proposed methods with comparison to existing procedures.