Foundations of Regression Graphics

摘要本研究的重点是如何利用实时的、计算密集型的、图形化的方法来研究回归问题的统计结构。它的前提是，如果没有良好的理论基础，就无法在回归分析中充分发挥现代计算机图形学的优势。重点放在基于降维子空间的回归图形的新兴理论的扩展和应用，以及该理论对标准图形结构解释的含义。以截尾生存时间作为响应的回归的图形基础得到了特别的关注。可视化统计数据的能力在分析复杂关系中起着重要作用。例如，衡量小学强制性考试的边际影响需要了解不同的社会经济环境如何影响表现。高性能计算（联邦战略领域之一）的最新进展为开发新的图形技术提供了机会，这些技术在适用性和能力上都远远超出传统图形。这项研究的中心是发现如何使用计算机图形学来调查复杂的统计关系。它源于这样一种观念，即即使在复杂的系统中，也可以构建易于理解的图形显示，其中包含数据中的所有或几乎所有相关信息。这种在易于理解的显示中保存信息的能力需要新的理论基础，这是本研究的一个组成部分。

DMS 9703777 Foundations of Regression Graphics Dennis Cook University of Minnesota ABSTRACT This research centers on finding how real-time, computationally intensive, graphical methods can be used to investigate the statistical structure of regression problems. It is based on the premise that the full benefit of modern computer graphics cannot be realized in regression analyses without sound theoretical foundations. Emphasis is placed on the expansion and application of an emerging theory for regression graphics based on dimension-reduction subspaces, and on the implications of this theory for the interpretation of standard graphical constructions. Graphical foundations for regressions with a censored survival time as the response are given special attention. The ability to visualize statistical data plays an important role in analyzing complex relationships. For example, a measure of the marginal impact of mandatory testing in grade schools requires understanding how different socioeconomic settings influence performance. Recent advances in high performance computing, one of the Federal Strategic Areas, allow for the opportunity to develop new graphical techniques that go far beyond traditional graphics in both applicability and power. This research centers on finding how computer graphics can be used to investigate complex statistical relationships. It stems from the notion that, even in complex systems, it is possible to construct easily understood graphical displays that contain all or nearly all of the relevant information in the data. This ability to preserve information in easily understood displays requires new theoretical foundations that are an integral part of this study.