Statistical Inference under Subjective and Not-Fully-Quantifiable Information on Experimental Units

在许多科学调查中，有大量关于实验材料的主观信息--哪些农田更肥沃，哪些病人更健康，等等--这是很难量化为一个正式的，数字变量进一步用于统计分析。 目前，统计科学无法有效地利用这些信息。 这项研究开发了一套技术，使人们能够恢复大部分信息，并以完全客观的方式使用它。 重要的是，同样的数学技术，适用于恢复的主观信息也允许人们利用“质量较低”的协变量，这可能会受到重大的测量误差或其他偏见。 这些质量较低的协变量用于在测量其响应之前在潜在实验单元之间创建人工分层。 作为这些技术基础的工作主体被称为排名集抽样。 排序集抽样的现状在非常强的假设下提供了理论基础，例如完美排序或其他精确指定的概率和判断排序模型。即使是一个小的偏离这些假设可能会导致不一致的估计，包含大量的偏见，甚至渐近。 有保留意见，在研究界关于使用排名集抽样时，无论是招募一个单位的研究成本是巨大的，或当可用的实验单位的数量是有限的。 在这些情况下，希望使用所有可用的实验单元来进行实验。 为了缓解这些问题，本研究着眼于从不同的角度来看，排名集抽样，并确定了三个领域，目前国家的最先进的排名集抽样是不合适的，表现不佳，或不能使用一个令人满意的一般方式。 这些领域是（i）在实验设计中使用排序集抽样，（ii）在最小判断建模假设下开发低和中等结构参数估计，以及（iii）开发排序过程的模型。这项研究将对统计分析产生重大影响，对科学研究的几个既定领域，对美国民众的生活质量，以及国家的科学基础设施。这项研究通过前段所述的机制，将使研究人员能够通过新颖的统计分析从实验中挤出更多的信息。 从实验中挤出更多信息的另一面是能够用较小的实验获得给定量的信息。 该研究将开发更好的设计来执行实验，影响各种学科。作为一个主要的例子，在新的设计中，用于确定新药益处的临床试验将需要更少的受试者。 审判费用将减少，审判将在更短的时间内完成。 更小、更便宜和更快的试验的三重好处将加快新药的开发和批准，包括那些治疗癌症等绝症的新药。 除了经济利益外，在不牺牲批准过程中现有保障措施的情况下，尽快通过开发过程推动有前途的新疗法也有伦理利益。 通过加强统计人员和医学研究人员之间的合作，以及通过严格培训研究生，将加强国家的科学基础设施。 将特别重视对妇女和少数民族进行数学方面的培训。

In many scientific investigations, there is a wealth of subjective information about experimental material--which agricultural plots are more fertile, which patients are healthier, etc.--that is difficult to quantify as a formal, numerical variate for further use in statistical analysis. Currently, statistical science is unable to effectively exploit this information. This research develops a body of techniques that allow one to recover the bulk of this information and to use it in a fully objective fashion. Importantly, the same mathematical techniques that apply to recovery of subjective information also allow one to exploit ``lesser quality'' covariates which may be subject to substantial measurement error or other biases. These lesser quality covariates are used to create an artificial stratification among the potential experimental units before their responses are measured. The body of work that underlies these techniques is known as ranked set sampling. The current status of ranked set sampling provides a theoretical foundation under very strong assumptions, such as perfect ranking or other precisely specified probability and judgment ranking models. Even a small departure from these assumptions may result in inconsistent estimators that contain substantial bias, even asymptotically. There are reservations within the research community regarding the use of ranked set sampling when either the cost recruiting a unit for a study is substantial or when the number of available experimental units is limited. In these situations, it is desirable to use all available experimental units to perform the experiment. To alleviate these concerns, this research looks at ranked set sampling from a different perspective and identifies three areas where the current state-of-the-art ranked set sampling is either not appropriate, performs poorly, or cannot be used in a satisfactory general fashion. These areas are (i) the use of ranked set sampling in the design of experiments, (ii) the development of low- and medium structure parametric estimation under minimal judgment modeling assumptions, and (iii)the development of models for the ranking process.This research will have a substantial impact on statistical analysis, on several established areas of scientific research, on the quality of life of the U.S. populace, and on the scientific infrastructure of the country. The research, through the mechanisms described in the preceding paragraph, will allow researchers to squeeze more information out of their experiments with novel statistical analyses. The flip side of squeezing more information out of an experiment is the ability to obtain a given amount of information with a smaller experiment. The research will develop better designs to perform experiments, impacting a wide variety of disciplines. As a prime example, with the new designs, a clinical trial, used to establish the benefits of a new drug, will require a smaller number of subjects. The cost of the trial will be reduced and the trial will be completed in a shorter time span. The triple benefit of a smaller, cheaper and quicker trial will expedite the development and approval of new drugs, including those for terminal diseases, such as cancer. In addition to economic benefits, there is the ethical benefit of moving promising new therapies through the development process as quickly as possible, without sacrificing current safeguards in the approval process. The scientific infrastructure of the country will be enhanced by the increased collaboration between statisticians and medical researchers, and by the rigorous training of graduate students. Particular emphasis will be given to the training of women and minorities in the mathematical sciences.