Semiparametic Efficient Inference Methods in Complex Data Models

复杂数据模型中的半参数高效推理方法

• 批准号: RGPIN-2016-06002
• 负责人: Wang, Liqun
• 金额: $ 2.4万
• 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=616041
• 关键词: Semiparametic; Efficient; Inference; Methods; Complex

Nowadays more and more massive and high-dimensional data become available in many scientific fields such as medical and health science, astronomy and physics, computer science and engineering, as well as economics and finance. A challenging task in high-dimensional data analysis is how to select the most relevant predictors among a large number of candidate variables to accurately predict a response variable of interest. High-dimensional variable selection problem has drawn a lot of attention in statistics, as well as in computer science and engineering. However, most research has been focusing on linear models where all variables are assumed to be precisely measured. On the other hand, real data applications always involve nonlinear relationships and variables that are either not directly observable or imprecisely measured. Therefore it is of theoretical and practical interests to study the high-dimensional variable selection problem in measurement error models. One possible direction of investigation is novel regularization methods that incorporate instrumental variables. Moreover, nonlinear relationships will be investigated because they arise in many fields including compressive sensing, signal processing and imaging. Survival and event history data analysis arises in many scientific disciplines including medical and health science, engineering, business and economics. However, the main stream methods rely on certain parametric or semiparametric models that have limited flexibility to model real life data. An alternative approach is based on an underlying stochastic process which, for example, represents an individual's health status. The event of interest occurs when this random process reaches a certain threshold for the first time. The first passage time has applications in many other disciplines including biology, chemistry, epidemiology, finance, and physics. However, the computation of the first passage time distributions is a challenging task. The proposed research will develop novel methods for calculation of the first passage time distributions. The new tools will provide much more flexible and general models for survival and event history data analysis. The proposed research will provide opportunities for the training of highly qualified personnel at all levels. They will be trained to be the experts in the areas that are currently very active and in the research fronts in statistics. Moreover, they will learn modern statistical theories and methodologies, and computational skills to deal with large scale and high-dimensional data. They will also learn to apply these methodologies and skills to solve real life problems.

如今，越来越多的海量、高维数据出现在医学与健康科学、天文学与物理学、计算机科学与工程、经济与金融等众多科学领域。高维数据分析中的一个具有挑战性的任务是如何在大量候选变量中选择最相关的预测变量来准确预测感兴趣的响应变量。高维变量选择问题引起了统计学以及计算机科学与工程领域的广泛关注。然而，大多数研究都集中在线性模型上，其中所有变量都被假设为精确测量。另一方面，实际数据应用总是涉及非线性关系和无法直接观察或不精确测量的变量。因此，研究测量误差模型中的高维变量选择问题具有重要的理论和实际意义。一个可能的研究方向是结合工具变量的新颖的正则化方法。此外，还将研究非线性关系，因为它们出现在许多领域，包括压缩传感、信号处理和成像。 生存和事件历史数据分析出现在许多科学学科中，包括医学和健康科学、工程、商业和经济学。然而，主流方法依赖于某些参数或半参数模型，这些模型对现实生活数据建模的灵活性有限。另一种方法基于潜在的随机过程，例如代表个人的健康状况。当这个随机过程第一次达到某个阈值时，就会发生感兴趣的事件。首次通过时间在许多其他学科中都有应用，包括生物学、化学、流行病学、金融和物理学。然而，首次通过时间分布的计算是一项具有挑战性的任务。拟议的研究将开发计算首次通过时间分布的新方法。新工具将为生存和事件历史数据分析提供更加灵活和通用的模型。 拟议的研究将为培训各级高素质人才提供机会。他们将被培训成为当前非常活跃的领域和统计学研究前沿的专家。此外，他们将学习现代统计理论和方法，以及处理大规模和高维数据的计算技能。他们还将学习应用这些方法和技能来解决现实生活中的问题。