回归模型中最优分配的一种有效计算算法
Efficient Computational Algorithm for Optimal Allocation in Regression Models
摘要：
本文讨论了一个实验中回归模型用于统计分析时的最优分配问题。文献中已经讨论了一类求解$D$ -最优性的乘法算法的单调收敛性。在这里，我们提供了一个替代的证明单调收敛的$D$ -准则与一个简单的计算算法，并进一步表明它收敛到$D$ -最优性。我们还讨论了$A$ -准则的单调收敛性的一个算法和一个猜想。蒙特卡罗模拟被用来证明所提出的算法的可靠性，效率和实用性。
英文摘要：
In this article, we discuss the optimal allocation problem in an experiment when a regression model is used for statistical analysis. Monotonic convergence for a general class of multiplicative algorithms for $D$-optimality has been discussed in the literature. Here, we provide an alternate proof of the monotonic convergence for $D$-criterion with a simple computational algorithm and furthermore show it converges to the $D$-optimality. We also discuss an algorithm as well as a conjecture of the monotonic convergence for $A$-criterion. Monte Carlo simulations are used to demonstrate the reliability, efficiency and usefulness of the proposed algorithms.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
