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

使用排名信息和顺序统计数据基于复杂的调查设计进行统计推断

• 批准号: RGPIN-2015-04157
• 负责人: JafariJozani, Mohammad
• 金额: $ 1.46万
• 依托单位: University of Manitoba
• 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=654430
• 关键词: Statistical; inference; based; complex; survey

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. ******* **

在许多实验中，实现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，或来自人群的廉价和有用的测量，这些信息可以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，考虑人口中骨矿物质密度的估计问题。这种研究的对象很多，但是通过双x线吸收仪对选定的对象进行骨矿物质密度测量是昂贵的。因此，重要的是在不减少获得有关人口骨矿物质密度构成的可靠信息的情况下，尽量减少此类研究所需的测量次数。一个成功的策略是利用大量采样单位的专家意见知识，从人群中确定更具代表性的样本，从这些样本中，应该通过双x射线吸收仪收集昂贵的骨密度测量。基于秩的抽样设计提供了一系列技术，可以在廉价信息的帮助下获得和分析这些昂贵的测量结果。这些设计已经应用于渔业、农业、环境和生态研究，如辐射（土壤污染和疾病集群）或污染（水污染和作物根病），以及医学研究、机器学习和图像处理。***本研究计划的重点是开发基于有限和无限种群中使用秩信息和顺序统计的复杂调查设计的参数和非参数推理的新方法。数学分析将提供对基于秩的数据的推理过程的洞察，并提出对此类样本进行有效推理的新方法。主要目标是从贝叶斯和频率论的角度回答涉及基于排名的数据的广泛研究问题。我还将研究考虑到排名器质量、排名器数量、样本量和排名类数量的优化机会。这项提案所带来的研究进展将有许多重要的应用。例如，加拿大统计局在设计基于排名信息的调查时可能会对结果感兴趣；向加拿大卫生部提供水质研究和环境风险监测；并感谢加拿大渔业和海洋部为监测与渔业有关的活动制定更好的方法。该建议不仅将补充和扩展现有的基于秩的抽样设计理论，而且还具有解决其他情况下观察涉及审查和/或长度偏差数据的方法学问题的潜力。******* **