Tomasz Zadlo

On some problems of estimation and prediction of domain total based on longitudinal data

In the presentation the accuracy of the empirical best linear unbiased predictor (EBLUP) of the  domain total is analyzed assuming a model for longitudinal data with subject specific (element specific) random components (compare: Verbeke, Molenberghs, 2000; Hedeker, Gibbons, 2006) with auxiliary information. The model is a special case of the general linear model (GLM) and the general linear mixed model (GLMM). The formula of the predictor is based on empirical version of Royall's (1976) predictor and it is shown that predictor presented by Henderson (1950) cannot be used in this case. To estimate the mean square error (MSE) of the  EBLUP we use the results obtained by Datta and Lahiri (2000) for the predictor proposed by Henderson (1950) and adopt them for the predictor proposed by Royall (1976) what was shown in some general case by ¯¹d³o (2009). The proposed solution can be used based on any longitudinal data (including random and purposive samples, panel data and rotating samples)  for any (including future) period even when the population, domains and the domain affiliation may change in time. In the presentation calibration estimators of subpopulation total for data from one period are presented too and some modifications for the case of longitudinal data are proposed. Design-based mean squared errors and its estimators are also presented. In the simulation study the problems of the accuracy of the predictor and biases of the proposed MSE estimator are analyzed including several cases of model misspecification. What is more, in the model-based and design-based simulations the accuracy of the predictor will be compared with accuracy of the considered calibration estimators.

Datta G. S. and Lahiri P. (2000). A unified measure of uncertainty of estimated best linear unbiased predictors in small area estimation problems. Statistica Sinica, 10, 613-627.
Hedeker D., Gibbons R.D. (2006), Longitudinal Data Analysis, John Wiley & Sons, Hoboken, New Jersey.
Henderson C.R. (1950). Estimation of genetic parameters (Abstract). Annals of Mathematical Statistics, 21, 309-310.
Royall R.M. (1976), The linear least squares prediction approach to two-stage sampling. Journal of the American Statistical Association, 71, 657-473.
Verbeke G., Molenberghs G. (2000), Linear Mixed Models for Longitudinal Data, Springer-Verlag, New York.
Zadlo T. (2009). On MSE of EBLUP, Statistical Papers, 50, 101-118.