Estimation procedures and optimal designs for estimation of the individual parameters and of the global parameters are discussed under various conditions of prior knowledge. The extension to nonlinear parametrization of the response function ís based on the asymptotical validity of the results for the linear parametrization. For the case where the error variance and the dispersion matrix are unknown, an iterative estimation procedure is suggested. An example based on dental plaque pH profiles demonstrates the improvement that is achieved (a) through using the optimal design or a design that ís close to the optimal, and (b) through taking into account prior information. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

The class of models which is studied in this paper, multi-unit longitudinal models, combines both the cross-sectional and the longitudinal aspects of observations. Many empirical investigations involve the analysis of data structures that are both cross-sectional (observations are taken on several units at a specific time period or at a specific location) and longitudinal (observations on the same unit are taken over time or space). Multi-unit longitudinal data structures arise in economics and business where panels of subjects are studied over time, biostatistics where groups of patients on different treatments are observed over time, and in situations where data are taken over time and space. Modelling issues in multi-unit longitudinal models with random coefficients and patterned correlation structure are illustrated in the context of two data sets. The first data set deals with short time series data on annual death rates and alcohol consumption for twenty-five European countries. The second data set deals with glaceologic time series data on snow temperature at 14 different locations within a small glacier in the Austrian Alps. A practical model building approach, consisting of model specification, estimation, and diagnostic checking, is outlined. (author's abstract) / Series: Forschungsberichte / Institut für Statistik

MSc (Physics) / Department of Physics

PhD (Physics) / Department of Physics / The knowledge of solar radiation in this dispensation is crucial. The lack of grid lines in the remote rural areas of South Africa necessitates the use of solar energy as an alternative energy resource. Solar radiation data is one of the primary factors considered for the installation of renewable energy devices and they are very useful for solar technology designers and engineers. In some developing countries, estimation of solar radiation becomes a challenge due to the lack of weather data. This scenario is also applicable to South Africa (SA) wherein there are limited weather stations and hence there is a dire need of estimating the global solar radiation data for all climatic regions. Using a five year global solar radiation (𝐻) and bright sunshine (𝑆) data from the Agricultural Research Council (ARC) and South African Weather Service (SAWS) in SA, linear Angstrom – Prescott solar empirical model was used to determine regression coefficients. MATLAB interface was used whereby the linear regression plots were drawn. Annual empirical coefficients of 22 stations were determined and later the provincial values. The range of the regression coefficients, a and b were 0.216 – 0.301 and 0.381 – 0.512 respectively. The 2006 estimated global solar radiation per station in a province calculated from the modified models were compared with the observed and statistically tested. The root mean square errors were less than 0.600 MJm−2day−1 while the correlation relation ranged from 0.782 – 0.986 MJm−2day−1. The results showed the regression coefficients performed well in terms of prediction accuracy. / NRF