Abstract:
This thesis considers Small Area Estimation with a main focus on estimation and prediction theory for repeated measures data. The demand for small area statistics is for
both cross-sectional and repeated measures data. For instance, small area estimates for
repeated measures data may be used by public policy makers for different purposes such
as funds allocation, new educational or health programs and in some cases, they might be
interested in a given group of population.
It has been shown that the multivariate approach for model-based methods in small
area estimation may achieve substantial improvement over the usual univariate approach.
In this work, we consider repeated surveys including the same subjects at different time
points. The population from which a sample has been drawn is partitioned into several
subpopulations and within all subpopulations there is the same number of group units. For
this setting a multivariate linear regression model is formulated. The aim of the proposed
model is to borrow strength across small areas and over time with a particular interest of
growth profiles over time. The model accounts for repeated surveys, group individuals
and random effects variations.
The estimation of model parameters is discussed with a restricted maximum likelihood based approach. The prediction of random effects and the prediction of small area
means across time points, per group units and for all time points are derived. The theoretical results have also been supported by a simulation study and finally, suggestions for
future research are presented.
