On MSE estimators of EBLUP of domain total under some longitudinal model

Abstract

Żądlo (2012) proposed a certain unit-level longitudinal model which was a special case of the General Linear Mixed Model. Two vectors of random components included in the model obey assumptions of simultaneous spatial autoregressive process (SAR) and temporal first-order autoregressive process (AR(1)) respectively. Moreover, it is assumed that the population can change in time and the population elements can change its domains’ (subpopulations’) affiliation in time. Under the proposed model, Żądlo (2012) derived the Empirical Best Linear Unbiased Predictor (EBLUP) of the domain total. What is more (based on the theorem proved by Żądlo (2009)), the approximate equation of the mean squared error (MSE) was derived and its estimator based on the Taylor approximation was proposed. The proposed MSE estimator was derived under some assumptions including that the variance-covariance matrix can be decomposed into linear combination of variance components. The assumption was not met under the proposed model. In the paper the jackknife MSE estimator for the derived EBLUP will be proposed based on the results presented by Jiang, Lahiri, Wan (2002). The bias of the jackknife MSE estimator will be compared in the simulation study with the bias of the MSE estimator based on the Taylor approximation.