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An efficient algorithm for Elastic I‐optimal design of generalized linear models
Author(s) -
Li Yiou,
Deng Xinwei
Publication year - 2021
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.1002/cjs.11571
Subject(s) - algorithm , equivalence (formal languages) , mathematical optimization , computer science , multiplicative function , generalized linear model , convergence (economics) , set (abstract data type) , mathematics , machine learning , mathematical analysis , discrete mathematics , economics , programming language , economic growth
The generalized linear models (GLMs) are widely used in statistical analysis and the related design issues are undoubtedly challenging. The state‐of‐the‐art works mostly apply to design criteria on the estimates of regression coefficients. The prediction accuracy is usually critical in modern decision‐making and artificial intelligence applications. It is of importance to study optimal designs from the prediction aspects for GLMs. In this work, we consider Elastic I‐optimality as a prediction‐oriented design criterion for GLMs, and develop an efficient algorithm for such EI‐optimal designs. By investigating theoretical properties for the optimal weights of any set of design points and extending the general equivalence theorem to the EI‐optimality for GLMs, the proposed efficient algorithm adequately combines the Fedorov–Wynn algorithm and the multiplicative algorithm. It achieves great computational efficiency with guaranteed convergence. Numerical examples are conducted to evaluate the feasibility and computational efficiency of the proposed algorithm.