Nonparametric Function Estimation

非参数函数估计

• 批准号: RGPIN-2015-04058
• 负责人: Leblanc, Alexandre
• 金额: $ 0.8万
• 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: 2016
• 资助国家: 加拿大
• 起止时间: 2016-01-01 至 2017-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=612749
• 关键词: Nonparametric; Function; Estimation

Statistical Function Estimation is extremely important in many areas of scientific research. At the heart of many problems is the need to construct a curve that summarizes some important aspect of a set of data, be it a histogram, a survival curve or a response curve. Doing this well is of utmost importance for experimenters, but also for administrators, decision makers and government officials of all kinds. It is often also important that the methods used and provided solutions be simple to interpret and generally valid, without imposing theoretical restrictions and/or assumptions that are difficult or even impossible to verify in practice. Linked to this is also the need for objective methodologies that are not too dependent on a specific form of model, again something that can be hard to justify. This objectivity takes many forms, but naturally leads to studying the so-called nonparametric methods of function estimation. For instance, one of the simplest examples of this is perhaps the study of linear regression problems. Two important aspects of how regression problems are often approached, are the requirement of normality for the random error distribution and the assumption that the relationship between the response variable and the measured covariates is linear. In some setups, the assumption of normality is known not to be met. In other setups, the relationship between the response variable and the measured covariates cannot be assumed to be linear, and in fact, cannot even be assumed to be known. A nonparametric solution to this problem would be to construct an estimate of the function linking the response variable to the covariates that does not assume any specific functional form (like linearity) and makes as few assumptions as possible about the distribution of the random error. The main thrust of this proposal is to develop and better understand nonparametric approaches, such as the one described above, to a range of different statistical function estimation problems. We study modern takes on some problems, which are especially relevant given the advent of big data. For instance, we consider some work on contingency tables in the context known as sparse asymptotics, where the complexity of problems grows as more data are collected. We also study a new family of functional regression models, where functions play the role of covariates. These models allow one to establish a link between a response variable and the full distribution of some population characteristics. Finally, we study the impact, on standard estimation methods, of using so-called rank-based sampling designs for data collection. We also develop new methods of function estimation specifically adapted to these alternate sampling plans.

统计函数估计在科学研究的许多领域都非常重要。许多问题的核心是需要构建一条曲线来总结一组数据的某些重要方面，无论是直方图、生存曲线还是响应曲线。做好这一点对实验者来说至关重要，对管理者、决策者和各类政府官员来说也是如此。同样重要的是，所使用的方法和所提供的解决办法应易于解释和普遍有效，而不施加难以或甚至不可能在实践中验证的理论限制和/或假设。与此相关的还有对客观方法的需求，这种方法不太依赖于特定形式的模型，这也是很难证明的。这种客观性有多种形式，但自然导致研究所谓的函数估计的非参数方法。