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Li, Y. and Deng, X. (2020), An efficient algorithm for Elastic I‐optimal design of generalized linear models. Can J Statistics. https://doi.org/10.1002/cjs.11571
Experimental design is to study how to efficiently design data collection, what inputs to collect data, for analysis and inference. When the output response is non-continuous, the generalized linear models are widely used as the key modeling tool for statistical analysis. However the related experimental design issues for generalized linear models becomes challenging due to the complication on the design criterion. The state-of-the-art works mostly focus on finding good designs for improving the estimates of regression coefficients. In modern data science, the prediction accuracy is often critical in decision making and artificial intelligence applications. Thus it is of great importance to study how to design optimal data collection from the prediction aspects for generalized linear models. In this work, the authors develop the so-called Elastic I-optimality as a prediction-oriented design criterion of data collection for generalized linear models. Moreover, the authors develop an efficient computation algorithm for finding such EI-optimal designs. By investigating theoretical properties for the optimal weights of any set of design points and establish the theoretical properties to the EI-optimality for GLMs, the proposed efficient algorithm adequately combines the sequential method and multiplicative algorithm. It achieves great computational efficiency with guaranteed convergence. The authors also conduct several numerical examples to evaluate the merits of the proposed method and elaborate the computational efficiency of the proposed algorithm.