Dynamic Signal Detection in Non- and Semi-Parametric Models

在大数据时代，具有复杂结构的海量数据以爆炸式的方式产生。非参数和半参数模型是探索隐藏在复杂数据中的非线性模式的强大统计工具，已被广泛应用于生物医学、地质学、工程学和社会科学等领域。然而，传统的非参数和半参数方法在处理高维海量数据时能力有限。本研究的目标是在大量复杂数据环境下，为非参数和半参数模型的动态估计和变量选择开发有效的工具。 拟议的研究产生了新的方法和理论，并将为不同领域的从业者提供工具，以更好地理解海量数据中复杂和动态的结构。变量选择作为一种有效的降维工具，对高维数据建模非常有用。近年来，对于线性模型和半参数模型，惩罚方法的性质得到了很好的研究。然而，这些方法通常不允许变量选择随其他变量动态变化。对于实践中的许多纵向数据或空间数据，有必要制定一个动态变量选择的总体框架，以便在不同的时间段或不同的空间位置选择可能不同的相关变量。本文的研究目标包括：（1）发展一种新的变系数模型中动态变量选择的方法：（2）提供大样本性质，以确保当样本容量足够大时，所提出的方法提供最优解;（3）开发一种有效的算法，即使协变量维数很大，也能获得较高的正确拟合率;（4）应用动态变量选择方法研究时变网络数据;（5）提出了一种新的三角剖分惩罚样条方法，该方法具有动态局部信号检测的作用，以及稀疏非线性的有效估计，该奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的知识产权评估的支持。优点和更广泛的影响审查标准。

In the big data era, massive data with complex structures are generated in an explosive fashion. Non- and semi-parametric models are powerful statistical tools for exploring nonlinear patterns hidden in complex data, and have been used in a wide range of fields, such as, biomedical science, geology, engineering and social sciences. However, traditional non- and semi-parametric methods are limited in their ability to deal with massive data of high dimensions. The goal of the proposed research is to develop effective tools for dynamic estimation and variable selection for non- and semi-parametric models in the massive complex data setting. The proposed research generates new methods and theory, and will provide practitioners in different fields with tools to better understand complex and dynamic structures in massive data. As an effective dimension reduction tool, variable selection is very useful for modeling high-dimensional data. In recent years, the properties of the penalized methods have been well investigated for both linear models and semiparametric models. However, those methods generally do not allow the variable selection to dynamically change with other variables. For many longitudinal or spatial data in practice, there is a need to develop a general framework for dynamic variable selection that allows possibly different sets of relevant variables to be selected in different time periods or at different spatial locations. The objectives of the proposed research include: (1) to develop a novel procedure for dynamic variable selection in the varying coefficient model; (2) to provide large sample properties to ensure that the proposed method provides an optimal solution when the sample size is sufficiently large; (3) to develop an efficient algorithm which allows one to obtain a higher percentage of correct-fitting even when the dimension of covariates is large; (4) to apply the dynamic variable selection to study time-varying network data ; (5) to develop an innovative penalized spline procedure with triangulations which plays the roles of dynamic local signal detection, as well as efficient estimation of sparse non-parametric functions on irregular domains.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.