Robust model discrimination designs and robust subsampling for big data regression

我打算继续研究与实验研究稳健设计相关的问题，同时将稳健性纳入大数据回归的子抽样策略中。“稳健性”通常指的是统计过程在与假设有轻微偏差的情况下保持其有效性的能力。近年来，稳健性在实验研究中被认为是一个重要的概念，在实验研究中，研究者通常基于模糊知识对生成数据的反应的结构做出假设。我感兴趣的是构建最优设计，即使拟合的模型只是一个近似值，也能保持其最优性。建议的研究包括三个研究问题。第一个研究问题是对我最近工作的补充，该工作是从科学学科模型歧视理论研究中的一个常见问题演变而来的。在假设真实模型位于竞争模型的Hellinger邻域的情况下，提出了构造稳健模型判别设计的方法。第二个研究问题是构造用于区分两个竞争模型的稳健设计的方法的推广，用于区分k个模型(其中k大于或等于2)。真实的模型可能是竞争模型中的一个，也可能不是其中一个竞争模型。第三个研究问题是大数据回归的稳健次抽样方法的研究。随着数据收集变得更容易，数据的绝对数量呈指数级增长。直接对这些史无前例的数据量进行统计分析是非常具有挑战性的，而二次抽样作为一种减少数据量的方法，已经引起了研究界的极大兴趣。然而，大多数用于大数据回归的次抽样方法依赖于拟合的回归模型。因此，研究这些次抽样方法对错误指定模型的稳健性并提出稳健的次抽样方法具有重要意义。

I intend to continue my investigation into problems related to the robust design of experimental studies, and meanwhile, incorporate robustness into subsampling strategies for big data regression. “Robustness” usually refers to the ability of a statistical procedure to retain its validity when there is a slight deviation from assumptions underlying the procedure.In recent years, robustness has been recognized as an important notion in experimental studies where the investigator usually makes an assumption about the structure of the response generating the data based on vague knowledge. My interest pertains to the construction of optimal designs which keep their optimality even when the fitted model is only an approximation. The proposed study consists of three research problems. The first research problem is a complement to my recent work, which evolved from a common problem in theoretical studies in scientific disciplines model discrimination. With the assumption that the true model is in one of the Hellinger neighbourhoods of the rival models, methods of constructing robust model discrimination designs will be proposed. The second research problem is an extension of methods of constructing robust designs for discriminating two rival models to the discrimination of k models with k being larger than or equal to 2. The true model may or may not be one of the rival models.The third research problem is an investigation of robust subsampling methods for big data regression. As collection of data becomes easier, the sheer volumes of data increase exponentially. Performing statistical analysis directly on these unprecedented volumes of data is extremely challenging, and subsampling, a method to reduce the size of data, has aroused a great deal of interest in the research world. However, most of the subsampling methods for big data regression depend on fitted regression models. Therefore, it is important to investigate the robustness of these subsampling methods against misspecified models and propose robust subsampling methods.