Adaptive Regression via Basis Selection from Multiple Libraries

本研究的目的是发展适应性更强的非参数和半参数方法。方法是使用多个库，并在选择过程中允许它们之间的融合。模型复杂性的数据驱动估计将被用来纠正自适应模型选择引起的偏差。将制定新的模式选择标准，使不同图书馆的基函数能够在平等的基础上竞争。对于扩展的线性模型，将提出广义协方差惩罚。由于模型复杂性是在选择过程的每个步骤中估计和合并的，因此所提出的方法是完全自适应的，因为它们动态地调整其策略以考虑要估计的函数的行为。所提出的程序是通用的，因为它们可以应用于任何类型库的组合，这些类型库可以包括傅立叶基、截断多项式基、样条基和小波基。该方法还在半参数模型中结合了变量选择和基选择，在许多领域收集了日益复杂的数据集。为了从数据中提取尽可能多的信息，强大的统计方法是必不可少的。计算能力的进步为建模人员提供了前所未有的机会，可以使用非参数和半参数建模技术来探索可能的隐藏结构。本提案中开发的新方法是自适应非参数和半参数建模程序的进步。这些方法和软件是相当通用的，可以应用于许多不同的领域，包括生物科学、经济学、工程学、地质和环境科学、信息技术、健康和医学、物理科学和社会科学。拟议的活动包括为未来的统计学研究人员培训研究生。私家侦探正在与环境、医学和社会科学领域的调查人员进行多项合作。一些建议的方法将被应用于分析正在进行的和未来的实验数据。这些程序将在R中执行，并将提供给全面R档案网。

The objective of this research is to develop more adaptive non-parametric and semi-parametric methods. The approach is to use multiple libraries and allow fusion among them in the selection process. Data-driven estimates of model complexities will be used to correct bias incurred by adaptive model selection. New model selection criteria will be developed to allow basis functions in different libraries to compete on an equal footing. The general covariance penalty will be developed for extended linear models. Since model complexities are estimated and incorporated at each step of the selection procedure, the proposed methods are fully adaptive in the sense that they dynamically adjust their strategy to take into account the behavior of the function to be estimated. The proposed procedures are general in the sense that they can be applied to combinations of any generic libraries which may include Fourier, truncated polynomial, spline and wavelet bases. The methods also combine variable selection with basis selection in a semi-parametric model.Increasingly complex data sets are being collected in many fields. Powerful statistical methods are essential for the extraction of as much information as possible from the data. Advances in computational power have afforded modelers unprecedented opportunities to exploit possible hidden structure using non-parametric and semi-parametric modeling techniques. The novel methodologies developed in this proposal constitute advances in adaptive non-parametric and semi-parametric modeling procedures. The methods and software are quite general which can be applied to a number of different fields including biological sciences, economics, engineering, geological and environmental sciences, information technology, health and medicine, physical sciences, and social sciences. The proposed activities involve training of graduate students for future researchers in statistics. The P.I. is engaged in several collaborations with investigators in the environmental, medical and social sciences. Some proposed methods will be applied to analyze data from ongoing and future experiments. The procedures will be implemented in R and will be contributed to the Comprehensive R Archive Network.