Robust and optimal design of experiments for models with possible misspecifications

实验在所有研究领域进行，以调查过程或系统。实验结果可以分析并用于优化工艺或系统。在工程和科学领域有许多应用。例如，实验在设计新产品、提高产品质量和可靠性、开发制造工艺以及优化系统或服务操作方面发挥着重要作用。实验优化设计是一个重要的研究领域，它关注的是有效和高效的实验设计。在接下来的五年中，我计划研究稳健估计方法，并针对各种模型错误规范的实验开发稳健和优化设计理论。在实践中，所提出的模型只是近似正确的，并且存在各种与模型假设的偏离，从而导致模型的错误规范。对于回归模型，在响应函数、误差方差、误差的自相关结构和误差的分布等方面都可能出现错误规范。我将学习稳健和最优设计准则，发展设计理论，探索新的数值算法，并为线性和非线性回归模型构建稳健和最优设计。优化设计和实验的结果将帮助我们在产品、流程、服务运营、政府政策等方面做出正确的决策。这项研究可以节省大量的宝贵资源，产生显著的社会效益和经济效益。

Experiments are performed in all fields of study to investigate processes or systems. Results from the experiments can be analyzed and used to optimize processes or systems. There are many applications in engineering and sciences. For example, experiments play an important role in designing new products, improving product quality and reliability, developing manufacturing processes, and optimizing systems or service operations. Optimal design of experiments is an important area of research which focuses on effective and efficient designs for experiments.In the next five years, I plan to investigate robust estimation methods and develop robust and optimal design theories for experiments with various model misspecifications. In practice, a proposed model is only approximately true, and there are various kinds of departures from the model assumptions which lead to model misspecifications. For a regression model, misspecifications can occur in the response function, the error variance, the auto-correlation structure of the errors and the distribution of the errors. I will study robust and optimal design criteria, develop design theories, explore new numerical algorithms, and construct robust and optimal designs for linear and nonlinear regression models. The results from optimal designs and experiments will help us make good decisions on products, processes, service operations, government policies and so on. This research may result in huge savings in valuable resources and generate significant social and economic benefits.