Semiparametic Efficient Inference Methods in Complex Data Models

如今，越来越多的海量高维数据被应用于许多科学领域，如医学和健康科学、天文学和物理学、计算机科学和工程以及经济学和金融学。在高维数据分析中，如何从大量候选变量中选择最相关的预测因子来准确预测感兴趣的响应变量是一个具有挑战性的任务。高维变量选择问题在统计学以及计算机科学和工程领域都受到了广泛的关注。然而，大多数研究都集中在线性模型上，假设所有变量都是精确测量的。另一方面，实际的数据应用总是涉及非线性关系和变量，这些关系和变量要么不能直接观察到，要么不能精确测量。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正则化方法。此外，非线性关系将被研究，因为它们出现在许多领域，包括压缩感知，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，这些模型对真实生活数据建模的灵活性有限。另一种方法是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。第一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、金融学和物理学。然而，第一次通过时间分布的计算是一项具有挑战性的任务。提出的研究将开发新的方法来计算首次通过时间分布。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度合格的人员提供机会。他们将接受培训，成为目前非常活跃的领域和统计研究前沿的专家。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。他们还将学习运用这些方法和技能来解决现实生活中的问题

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.**