Statistical inference based on complex survey designs using rank information and order statistics

在许多实验中，实施统计上合理的抽样设计的一个重要因素是从抽样单位进行测量的成本。有时，研究人员可以获得一些辅助信息，或早期调查的结果、专家意见知识，或来自总体的廉价而有用的测量，这些测量可用于在对抽样单位进行最终测量之前轻松地对其进行排序。例如，考虑人类群体中骨密度的估计问题。这类研究的对象很多，但在选定的对象上通过双X射线骨密度仪测量骨密度是昂贵的。因此，在不减少获得有关人群骨密度构成的可靠信息量的情况下，最大限度地减少此类研究所需的测量次数是很重要的。一种成功的策略是利用专家对大量采样单位的意见知识，从人群中识别更具代表性的样本，其中昂贵的骨密度测量应该通过双X-射线吸收法收集。基于等级的抽样设计提供了一系列技术，以在廉价信息的帮助下获得和分析这些昂贵的测量。这些设计已在渔业、农业、环境和生态研究中得到应用，例如辐射(土壤污染和疾病群)或污染(水污染和作物根病)，以及在医学研究、机器学习和图像处理中。 这项研究计划致力于开发基于复杂调查设计的参数和非参数推断的新方法，这些设计使用有限和无限总体中的秩次信息和顺序统计量。数学分析将提供对基于排名的数据的推理过程的洞察，并为使用此类样本进行有效推理提出新的方法。主要目的是从贝叶斯和频数的角度回答涉及基于排名的数据的广泛研究问题。我还将研究考虑排名者质量、排名者数量、样本量和排名班数的优化机会。 这一提议带来的研究进展将有许多重要的应用。例如，在设计基于等级信息的调查时，加拿大统计局可能会感兴趣；加拿大卫生部会对水质研究和环境风险监测感兴趣；以及加拿大渔业和海洋局会制定更好的方法来监测与渔业有关的活动。这一提议不仅将补充和扩展现有的基于排名的抽样设计理论，而且还有可能解决其他情况下的方法学问题，这些情况下的观测涉及审查和(或)长度偏向的数据。

In many experiments, an important factor in implementing a statistically sound sampling design is the cost of taking measurements from sampling units. Sometimes researchers have access to some auxiliary information, or results of earlier surveys, expert-opinion knowledge, or inexpensive and useful measurements from the population that can be used to easily rank sampling units prior to taking final measurements on them. For example, consider the problem of estimation of bone mineral density in a human population. Subjects for such a study are plentiful, but measurement of bone mineral density via dual x-ray absorptiometry on the selected subjects is expensive. Thus, it is important to minimize the number of measurements required for such a study without reducing the amount of reliable information obtained about the bone mineral density makeup of the population. One successful strategy is to use expert-opinion knowledge on a large number of sampling units to identify more representative samples from the population from which the expensive bone mineral density measurement should be collected via dual x-ray absorptiometry. Rank-based sampling  designs provide a collection of techniques to obtain and analyze these expensive measurements with the help of inexpensive information.  These designs have found applications in fisheries, agricultural, environmental and ecological studies such as radiation (soil contamination and disease clusters) or pollution (water contamination and root disease of crops)  as well as in medical research, machine learning and image processing. This research proposal focuses on developing new methodologies for parametric and nonparametric inference based on complex survey designs using rank information and order statistics in finite and infinite populations. The mathematical analysis will provide insight into the process of inference from rank-based data and suggest  new methodologies for efficient inference with such samples. The main objective is to answer broad research problems involving rank-based data from both the Bayesian and frequentist perspectives. I will also study the optimization opportunities that take into account quality of rankers, number of rankers, sample size and number of ranking classes. The research developments coming from this proposal will have many important applications. For example, the results could be of interest to Statistics Canada when designing surveys based on rank information; to Health Canada for water quality studies and environmental risk monitoring;  as well as to Fisheries and Oceans Canada for developing better methods for monitoring fisheries-related activities. The proposal would not only complement and extend the existing theory on rank-based sampling designs, but also has the potential to address methodological problems in other settings where observations involve censored and/or length-biased data.