Algorithm for Bounded Optimal Design for General Nonlinear Model and Subdata Selection on Big Data

With the development of modern information technologies, nowadays a tremendous quantity of data is being collected with the potential to enhance our lives, and technologies and to offer people unprecedented scientific breakthroughs. On the other hand, the enormous scale of datasets presents new difficulties in analyzing them. Recently, various data reduction methods have been proposed to address the issue of excessive data volume. However, how does one measure the performance and statistical efficiency, of a selected method accurately? An ideal solution is to derive an optimal subdata. Unfortunately, as a typical NP-hard problem, given the large size of full data, it is infeasible to derive such optimal subdata. However, we can derive a nearly optimal subdata through Approximate Bounded Optimal Design (ABOD). In this dissertation, we aim to develop a general algorithm, the Group Exchange Algorithm, for ABOD. It can be used to select a nearly optimal subdata from any given full data set under both linear and non-linear models regardless of optimality criterion and parameters of interest. We also derive an equivalence theorem for ABOD and prove the convergence of the GE algorithm. Our simulation studies show that under different model settings, parameters of interest, size of the full data, and upper bounds for subdata selection, our algorithm keeps its outstanding performance compared to other methods.