Robust model discrimination designs and robust subsampling for big data regression

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I intend to continue my investigation into problems related to the robust design of experimental studies, and meanwhile, incorporate robustness into subsampling strategies for big data regression. “Robustness” usually refers to the ability of a statistical procedure to retain its validity when there is a slight deviation from assumptions underlying the procedure.***In recent years, robustness has been recognized as an important notion in experimental studies where the investigator usually makes an assumption about the structure of the response generating the data based on vague knowledge. My interest pertains to the construction of optimal designs which keep their optimality even when the fitted model is only an approximation. The proposed study consists of three research problems. ***The first research problem is a complement to my recent work, which evolved from a common problem in theoretical studies in scientific disciplines – model discrimination. With the assumption that the true model is in one of the Hellinger neighbourhoods of the rival models, methods of constructing robust model discrimination designs will be proposed. The second research problem is an extension of methods of constructing robust designs for discriminating two rival models to the discrimination of k models with k being larger than or equal to 2. The true model may or may not be one of the rival models.***The third research problem is an investigation of robust subsampling methods for big data regression. As collection of data becomes easier, the sheer volumes of data increase exponentially. Performing statistical analysis directly on these unprecedented volumes of data is extremely challenging, and subsampling, a method to reduce the size of data, has aroused a great deal of interest in the research world. However, most of the subsampling methods for big data regression depend on fitted regression models. Therefore, it is important to investigate the robustness of these subsampling methods against misspecified models and propose robust subsampling methods.