Robust model discrimination designs and robust subsampling for big data regression

用于大数据回归的稳健模型判别设计和稳健子采样

• 批准号: RGPIN-2018-04451
• 负责人: Hu, Rui
• 金额: $ 1.17万
• 依托单位: Grant MacEwan University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2018
• 资助国家: 加拿大
• 起止时间: 2018-01-01 至 2019-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=653965
• 关键词: Robust; model; discrimination; designs; robust

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.

我打算继续研究与实验研究的稳健设计相关的问题，同时将稳健性纳入大数据回归的子采样策略。“稳健性”通常是指统计程序在与程序所依据的假设略有偏差时保持其有效性的能力。近年来，鲁棒性已被公认为是实验研究中的一个重要概念，研究者通常基于模糊知识对生成数据的响应结构进行假设。我的兴趣涉及到建设的最佳设计，保持其最优性，即使当拟合模型只是一个近似。该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，它是从科学学科理论研究中的一个常见问题-模型歧视演变而来的。假设真实模型是在竞争对手的模型的Hellinger邻域之一，构造鲁棒模型判别设计的方法将被提出。第二个研究问题是将构造区分两个竞争模型的稳健设计的方法推广到区分k个模型，其中k大于或等于2。真正的模型可能是也可能不是竞争对手的模型之一。第三个研究问题是大数据回归的鲁棒子采样方法的研究。随着数据收集变得越来越容易，数据量呈指数级增长。直接对这些前所未有的数据量进行统计分析是极具挑战性的，而子采样，一种减少数据大小的方法，在研究界引起了极大的兴趣。然而，大多数大数据回归的子采样方法都依赖于拟合的回归模型。因此，重要的是研究这些子采样方法对错误指定的模型的鲁棒性，并提出鲁棒的子采样方法。