Optimal Designs In Random Coefficient Regression Models

The thesis is concerned with optimal designs in identical designs based on D-, G-, A-, I- andDβ- optimality criteria for several random coefficient regression models.For single variable random coefficient regression models, optimal designs are investigatedwhen the errors with both homogeneous and heteroscedastic structures. Explicit expressions ofD-, G-, A-, I- and Dβ- optimal designs in single variable random coefficient regression modelswith homogeneous errors are obtained on general closed intervals. For single variable random co-efficient regression models with heteroscedastic errors, a less restrictive sufficient condition of theheteroscedastic structure is given to make sure that the search of optimal designs can be confinedat extreme settings of the unit design region. Analytical solutions of D-, G-, A-, I- and Dβ- op-timal designs in single variable random coefficient regression models with heteroscedastic errorsare given. Optimal designs in random slope and random intercept models with heteroscedastic er-rors both are discussed in details. Some examples of random slope models and random interceptmodels with specific heteroscedastic errors are present. The results could be extended on generalclosed intervals.For bivariate random coefficient regression models, our attention is to dedicate optimal de-signs on the unit square design region under homogeneous errors and heteroscedastic errors. Forhomogeneous structure, we get that optimal designs can be confined at extreme settings of theunit square, analytical solutions of optimal designs are obtained. The result could be extended onclosed rectangle regions. For bivariate random coefficient regression models with heteroscedasticerrors, a less restrictive sufficient condition of the heteroscedastic structure is given to make surethat the search of optimal designs can be confined at extreme settings of the unit square. Opti-mal designs in bivariate random coefficient regression models with three different heteroscedasticerrors are discussed, numerical results of optimal designs in these models are present.In the last, DS- optimal design in single variable random coefficient regression models is dis-cussed. On closed interval design regions, it is certificated that there exists no DS- optimal designin single variable random coefficient regression models. Less restrictive sufficient conditions aregiven to make sure that equireplicated design is DS- optimal design for single variable regressionmodels with heteroscedastic errors.