Contributions to reduced rank modelling with applications to small area estimation
This dissertation focuses on the problem of decomposing residuals in the GMANOVAMANOVA models with rank restrictions on parameters with applications in small area estimation. Firstly, residuals in the GMANOVA-MANOVA model with rank restrictions on the mean parameters is considered. The main objective is to define residuals useful for evaluating the reduced rank restriction model. We decompose linear spaces into four subspaces as it can be done for the Extended Growth Curve model with two "profiles". The new residuals are defined by orthogonal projections on these subspaces. It is discussed how the new residuals can be used to test model assumptions. Secondly, survey data from Uganda, including the 2014 Uganda Population and Housing Census data have been analysed using small area estimation methodology. The GMANOVA-MANOVA model with rank restrictions on parameters was used to estimate the small area means. The aim of the analysis was to assess change over time in household living standards (welfare). We investigated whether households displayed growth in living standards; whether households grew at the same rates; and whether households in different geographical areas of the country grew at the same rates. The analysis shows that growth in household standards of living in Uganda varied across small areas. It was found that the sub-regions (small areas), with the highest standards of living in Uganda at the endline were Central Urban, Kampala and South Western Urban. While the sub-regions with the lowest standards of living at the endline were North East Rural, North East Urban and Eastern Rural. The sub-regions with the highest growth rates in standards of living were Mid West Urban, Mid North Rural, and South Western Urban. The sub-regions with the highest decline in standards of living were East Central Rural, East Rural and West Nile Urban.