Multivariate Analysis, Ranks, and Multivariate Ranks

多元分析、排名和多元排名

• 批准号: 0071757
• 负责人: John Marden
• 金额: $ 7.49万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-08-01 至 2004-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0071757&HistoricalAwards=false
• 关键词: Multivariate; Analysis; Ranks

The project explores two areas that utilize ranked data. The first aims to develop statistical procedures that are robust to violations of assumptions while still working close to optimally when the assumption holds. There is a long history of such robust procedures based on ranking the data, that is, replacing the observed values in the data with the values' ranks. This process helps to ameliorate the effects of unusually wild observations that can ruin an analysis. A number of multivariate situations in which there has previously been little work using rank procedures will be the main focus of this project. These include certain structural models defining the relationship of variables, testing for runs in multivariate data observed over time, estimating variances and covariances, and testing whether certain variables are conditionally independent given some other variables. A proposed method for defining multivariate ranks ("iterated ranks") so that their distribution is independent of the distribution of the underlying observations will be explored.The second area looks at modeling rank data directly, where the data arise from judges ranking particular objects based on their preferences. One popular model posits that judges and objects can be arrayed along a line, where a judge is located nearest the judge's most preferred object, next closest to the second most preferred object, etc. A new model that also allows judges to locate themselves nearest the objects they prefer least will be considered. An extension of these models in which there is provision for a small percentage of judges to act not at all according to the model will also be considered.

该项目探索了利用排名数据的两个领域。第一个目标是开发统计程序，使其对假设的违反具有鲁棒性，同时在假设成立时仍然接近最优。这种基于数据排序的稳健程序由来已久，也就是说，用数据中的观测值替换这些值的排名。这一过程有助于改善可能破坏分析的异常异常的观察结果的影响。一些以前很少使用秩过程的多变量情况将是这个项目的主要焦点。这些包括定义变量关系的某些结构模型，在一段时间内观察到的多变量数据中测试运行，估计方差和协方差，以及在给定其他变量的情况下测试某些变量是否有条件独立。本文将探讨一种定义多元秩（“迭代秩”）的建议方法，使其分布独立于基础观测值的分布。第二个领域着眼于直接建模排名数据，其中数据来自法官根据他们的偏好对特定对象进行排名。一个流行的模型假设法官和物体可以沿着一条线排列，其中法官位于离法官最喜欢的物体最近的地方，其次靠近第二喜欢的物体，等等。一种新的模式也将允许法官将自己定位到离他们最不喜欢的物体最近的地方。还将考虑扩大这些模式，其中规定一小部分法官完全不按照该模式行事。