Random Coefficients Of Regression Model I_l - Optimal And R - Optimal Design

The thesis is concerned with optimal designs based on IL? and R-criterion for random coefficient regression models. IL? and R? optimalcriterion are put forward respectively from the angle of predictionprecision and the simultaneous interval estimation precision. With thegeneral equivalence theorem established, the article proposed theiterative algorithms, and find the approximate IL? and R-optimal designthrough programming. On the research of the IL? optimal design ofuniresponse random coefficient regression model, a general model isdefined. With the covariance matrix known, we constructed the IL?optimal criterion and the general equivalence theorem, and proposedthe corresponding iterative algorithm. For the one or two orderpolynomial random coefficient model, we provided some propertiesabout the IL? optimal criterion. we can use such iterative algorithm, getthe numerical results through Matlab and use the following graphics toverify the feasibility of the iterative algorithm. On the research of the IL?optimal design of multiresponse random coefficient regression model,the general form of multiresponse random coefficient regression modelwas defined. With the covariance matrix of the vector of the randomcoefficient and the vector of random error known, we constructed thethe IL? optimal criterion and the general equivalence theorem, andproposed the corresponding iterative algorithm. Some numericalexamples were given to verify the feasibility of algorithm. On theresearch of the R? optimal design of uniresponse random coefficientregression model, the simultaneous confidence interval about unknownparameter was constructed by the Bonferroni method. We constructedthe R-optimal criterion according to this simultaneous confidenceinterval. With the covariance matrix known, we constructed the generalequivalence theorem and the iterative algorithm. Some numerical examples were given to verify the feasibility of algorithm. Consequently,the paper has deep researches on several areas of IL? and R? optimaldesigns for random coefficient regression models. With thedevelopment of experiment design, for these there are many aspectsto be studied.