CAREER: Model Selection for Semiparametric Regression Models in High Dimensional Modeling and its Oracle Properties

建议：DMS 0348869PI：Runze Li研究所：宾夕法尼亚州立大学高维建模中半参数回归模型的模型选择及其Oracle属性摘要模型选择是高维数据分析的基础，半参数回归模型在高维数据分析中具有潜在的实用价值。半参数回归模型的模型选择包括两个部分：非参数部分的模型选择(如平滑参数的选择)和参数部分的变量选择。传统的变量选择方案，如逐步删除法和最佳子集变量选择法，可以推广到半参数建模，但由于它们需要为每个子模型选择平滑参数，因此计算量较大。这一建议的目的是为三类半参数模型开发新的广泛适用的模型选择程序，为文献中现有的任何半参数回归模型提供一个统一的框架。在这个方案中，PI(A)研究了所提出的估计量的渐近行为，(B)证明了结果估计量的收敛速度如何依赖于正则化参数，(C)证明了所提出的方法在半参数回归模型的变量选择中的表现与Oracle方法一样好，以及(D)解决了与所提出的方法的实施有关的问题。PI还通过广泛的蒙特卡罗模拟研究来检验有限的样本性能，并将所提出的程序应用于实际数据的分析。借助现代数据采集设备和巨大的数据存储空间，人们可以轻松地收集高维数据，如生物技术数据、金融数据、卫星图像和高光谱图像。高维数据的分析对统计学家提出了许多挑战，正在成为统计学中最重要的研究课题。这一建议(A)为高维数据分析中半参数回归建模的模型选择奠定了基础和全面的框架，(B)对未来高维统计建模的研究具有重大影响，(C)显著增强了用于高维统计建模的统计工具和软件的可用性。拟议的工作还使不同领域的广泛科学家和研究人员受益，包括汽车工程、医学研究、预防研究、公共卫生和社会科学。

proposal: DMS 0348869PI: Runze Liinstitution: The Pennsylvania State UniversityModel Selection for Semiparametric Regression Models in HighDimensional Modeling and its Oracle Properties AbstractModel selection is fundamental to high-dimensional data analysis, andsemiparametric regression models are potentially useful for analysis ofhigh-dimensional data. Model selection for semiparametric regressionmodels consists of two components: model selection (such as choice ofsmoothing parameters) for the nonparametric component, and variable selectionfor the parametric portion. Traditional variable selectionschemes, such as the stepwise deletion and the best subset variableselection, could be extended to semiparametric modeling, but they areexpensive in computation since they require the smoothing parameters tobe selected for each submodel. The objectives of this proposal are todevelop new widely applicable model selection procedures for threeclasses of semiparametric models which provide a unified framework formany existing semiparametric regression models in the literature. In thisproposal, the PI (a) studies the asymptotic behaviors of the proposedestimators, (b) demonstrates how the rate of convergence of the resultingestimator depends on the regularization parameter, (c) shows that the proposedprocedures perform as well as the oracle procedure in variable selectionfor semiparametric regression models, and (d) addresses issues related toimplementation of the proposed procedures. The PI also examines finitesample performance via extensive Monte Carlo simulation studies andapplies the proposed procedures to analysis of real data.With modern data collection devices and vast data storage space, one caneasily collect high-dimensional data, such as biotech data, financial data,satellite imagery and hyperspectral imagery. Analysis of high-dimensionaldata poses many challenges for statisticians and is becoming the mostimportant research topic in statistics. This proposal (a) lays downa well-grounded and comprehensive framework for model selection forsemiparametric regression modeling in high-dimensional data analysis,(b) has significant impact on the future research of high-dimensionalstatistical modeling, and (c) enhances significantly the availabilityof statistical tools and software for high-dimensional statistical modeling.The proposed work is incorporated into a new topic course from whichgraduate students may directly benefit. The proposed work alsobenefits a broad range of scientists and researchers in various fields, includingautomotive engineering, medical studies, prevention studies, public healthand social sciences.