Optimal and Robust Designs for Regression

最优且稳健的回归设计

• 批准号: RGPIN-2015-03856
• 负责人: Xu, Xiaojian
• 金额: $ 0.8万
• 依托单位: Brock 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=669090
• 关键词: Optimal; Robust; Designs; Regression

The main objective of this research program is to understand how the nature of designs of experiments affects the results of estimation, prediction, and extrapolation in regression for various models assumed with or most likely without accuracy and to develop theory and methods of constructing regression designs that provide efficient results with optimized balance between precision in estimates and protection from possible model departures.****The areas of generalized linear fixed models (GLM), generalized linear mixed models (GLMM), accelerated life testing (ALT), and quantile regression have attracted much research activity. Significant results on optimal and robust designs for GLM, GLMM, and ALT have been obtained under my current grant. Recently, we have also achieved important results for analysis of weighted quantile regression (WQR) but not yet explored its design issue. This proposal aims to primarily build upon design construction for GLM, GLMM, ALT, and innovatively develop theory and methods of design construction for WQR. ****For GLM:***I will continue working on constructing robust design, using newly developed methods, for general GLM with possible overdispersion and inaccuracies in the assumed linear predictor, in model parameter specification, and in the assumed link function.****For GLMM:***Building on my earlier work for constructing optimal design for GLMM, I will explore robust design methods for GLMM with possible misspecified random effects distribution and inaccuracy in the assumed linear predictor. Both model parameter estimation and the Fisher information calculation for GLMM are often challenging, especially when multiple random effects or a multidimensional design space is involved. Hence, I will also investigate the computational issues concerned.****For ALT:***Whereas previous research on optimal and robust design for ALT has mainly focused on parametric models, I plan to construct optimal and robust design for ALT for a commonly used semi-parametric model - a proportional hazard model (PHM). The assumed baseline hazard function in a PHM is often with uncertainty due to the extrapolation nature of ALT and the resulting optimal deigns often depend on PHM parameters. Therefore, I will also construct robust deigns against possible misspecification in the assumed baseline hazard function and in the initial parameter values.****For WQR:***The most important virtue of quantile regression is its capability to make inferences on the entire conditional response distribution. However, there is minimal literature (all considered classical quantile regression) addressing optimal and robust design problems for quantile regression. It has been shown that WQR is an important method to improve the performance of statistical analysis for quantile regression, especially when heteroscedasticity is present. Hence, I will also develop theory and methods of optimal and robust designs for WQR.**

本研究计划的主要目标是了解实验设计的性质如何影响回归中各种模型的估计、预测和外推结果，这些模型假设有或很可能没有准确性，并发展构建回归设计的理论和方法，以提供有效的结果，并在估计精度和防止可能的模型偏离之间取得最佳平衡。****广义线性固定模型（GLM）、广义线性混合模型（GLMM）、加速寿命试验（ALT）和分位数回归等领域吸引了大量的研究活动。在我目前的资助下，GLM、GLMM和ALT的优化和稳健设计取得了重大成果。近年来，我们在加权分位数回归（weighted quantile regression， WQR）的分析方面也取得了重要的成果，但尚未探讨其设计问题。本课题旨在以GLM、GLMM、ALT的设计构建为基础，创新发展WQR的设计构建理论和方法。****对于GLM:***我将继续致力于构建稳健设计，使用新开发的方法，对于一般GLM，在假设的线性预测器，模型参数规范和假设的链接函数中可能存在过分散和不准确性。****对于GLMM:***在我早期构建GLMM优化设计工作的基础上，我将探索GLMM的鲁棒设计方法，该方法可能具有错误指定的随机效应分布和假设的线性预测器中的不准确性。GLMM的模型参数估计和Fisher信息计算往往具有挑战性，特别是当涉及多个随机效应或多维设计空间时。因此，我也将研究有关的计算问题。****对于ALT:***鉴于以往关于ALT优化稳健设计的研究主要集中在参数模型上，我计划针对一种常用的半参数模型——比例风险模型（PHM）构建ALT的优化稳健设计。由于ALT的外推性质，PHM中假定的基线危险函数通常具有不确定性，并且最终的最佳设计通常依赖于PHM参数。因此，我还将构建健壮的设计，以防止在假设的基线危险函数和初始参数值中可能出现的错误规范。****对于WQR:***分位数回归最重要的优点是它能够对整个条件反应分布进行推断。然而，很少有文献（都被认为是经典的分位数回归）解决了分位数回归的最优和稳健设计问题。研究表明，WQR是提高分位数回归统计分析性能的重要方法，特别是在存在异方差的情况下。因此，我也将发展WQR最优稳健设计的理论和方法