Different Types Of Random Coefficients Of Variance Optimal Design Regression Model

This thesis is concerned with the optimal design for the single variable random coefficien-t heteroscedastic regression model and bivariate random coefficient heteroscedastic regressionmodel, mainly discusses D optimal design, G optimal design, A optimal design, V optimaldesign, E optimal design and the efficiency of these kinds of optimal designs.For single variable random coefficient regression model, we assume that the random slopeand the random intercept related. Besides, the random errors are heteroscedastic. we proved thatwhen the random errors variance function satisfy a given condition, the search of D optimaldesign, G optimal design, A optimal design,V optimal design, E optimal design can beconfined at extreme settings of the design region. At the same time, we got show expression ofD optimal design, G optimal design, A optimal design and V optimal design.But we canonly get numerical results of E optimal design. What’s more, we gave the definition of somekinds of design, numerical results of optimal designs in the single variable random coefficientregression model are present.For bivariate random coefficient regression model, assuming that the random coefficient be-tween two related and the random errors are heteroscedastic too. We also proved that when therandom errors variance function satisfy a given structure, the search of D optimal design can beconfined at the extreme setting of design region.