Using SeDuMi to find various optimal designs for regression models.
Using SeDuMi to find various optimal designs for regression models.
复制标题
使用 SeDuMi 寻找回归模型的各种最佳设计。
DOI：
10.1007/s00362-017-0887-7
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Zhou,Julie
中科院分区：
文献类型：
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作者：
Wong,WengKee;Yin,Yue;Zhou,Julie
我们介绍了一个强大的，但很少使用的数值方法在统计学解决一类优化问题，其中搜索空间是离散的。这种优化工具被广泛应用于工程中求解半定规划问题，称为自对偶最小化。我们以最优设计问题为重点，演示了如何将A-、A-、c-、I-和l -最优设计问题表述为SDP问题，并展示了如何在MATLAB中使用SeDuMi有效地求解这些问题。我们还通过将数值方法应用于基于加权最小二乘估计的进一步寻找最优设计或当所寻求的最优设计的权重分布有约束时，表明了数值方法的灵活性。对于近似设计，sdp生成的设计的最优性可以用Kiefer-Wolfowitz等价定理来验证。SDP还发现了社会和生物医学研究中常用的非线性回归模型的最佳设计。给出了线性和非线性模型的几个例子。
We introduce a powerful and yet seldom used numerical approach in statistics for solving a broad class of optimization problems where the search space is discretized. This optimization tool is widely used in engineering for solving semidefinite programming (SDP) problems and is called self-dual minimization (SeDuMi). We focus on optimal design problems and demonstrate how to formulate A-, A-, c-, I-, and L-optimal design problems as SDP problems and show how they can be effectively solved by SeDuMi in MATLAB. We also show the numerical approach is flexible by applying it to further find optimal designs based on the weighted least squares estimator or when there are constraints on the weight distribution of the sought optimal design. For approximate designs, the optimality of the SDP-generated designs can be verified using the Kiefer–Wolfowitz equivalence theorem. SDP also finds optimal designs for nonlinear regression models commonly used in social and biomedical research. Several examples are presented for linear and nonlinear models.