Optimal Design for Nonlinear Model with Random Effect and Information-Based Subdata Selection for LASSO

Optimal designs for nonlinear model with random block effects are systematically studied. For a large class of nonlinear models, we prove that any optimal design can be based on some simple structures. We further derive the corresponding general equivalence theorem. This result allows us to propose an efficient algorithm of deriving specific optimal designs. The application of the algorithm is demonstrated through deriving a variety of locally optimal designs and accessing their robustness under different nonlinear models. Extraordinary amounts of data are being produced in many branches of science as well as people’s daily activity. Such data are usually huge in both rows and columns. Modeling such data with limited computation resource has been a challenging problem. We propose an approach select a very informative subset of the data based on optimal design theory, using LASSO regression to perform variable selection and estimation. Compare to exist methods like balanced or weighted sampling, our approach avoids involving sampling error and thus provides more accurate estimation/prediction, also takes much less time.