EI-Optimal Design: An Efficient Algorithm for Elastic I-optimal Design of Generalized Linear Models
EI-Optimal Design: An Efficient Algorithm for Elastic I-optimal Design of Generalized Linear Models
复制标题
EI 最优设计：广义线性模型弹性 I 最优设计的有效算法
DOI：
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发表时间：
2018
期刊：
影响因子：
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通讯作者：
Xinwei Deng
中科院分区：
文献类型：
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作者：
Yiou Li;Xinwei Deng
广义线性模型（GLMs）在统计分析中广泛应用，相关的设计问题无疑具有挑战性。最前沿的研究工作大多适用于回归系数估计的设计准则。从广义线性模型的预测方面研究最优设计是很重要的。在这项工作中，我们将弹性I - 最优性视为广义线性模型的一种面向预测的设计准则，并为此类EI - 最优设计开发高效算法。通过研究任意一组设计点的最优权重的理论性质，并将一般等价定理推广到广义线性模型的EI - 最优性，所提出的高效算法充分结合了费多罗夫 - 温恩算法和乘法算法。它在保证收敛性的同时实现了很高的计算效率。通过数值例子评估了所提出算法的可行性和计算效率。
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. It is of importance to study optimal designs from the prediction aspects for generalized linear models. In this work, we consider the Elastic I-optimality as a prediction-oriented design criterion for generalized linear models and develop efficient algorithms 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 multiplicative algorithm. It achieves great computational efficiency with guaranteed convergence property. Numerical examples are conducted to evaluate the feasibility and computational efficiency of the proposed algorithm.