Adaptive Regression via Basis Selection from Multiple Libraries

本研究的目的是发展更具适应性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。数据驱动的模型复杂性估计将用于纠正自适应模型选择引起的偏差。我们会制定新的模式选择准则，让不同图书馆的基函数在平等的基础上竞争。一般协方差惩罚将用于扩展线性模型。由于模型复杂性在选择过程的每一步都被估计和纳入，因此所提出的方法在动态调整策略以考虑待估计函数的行为的意义上是完全自适应的。所提出的程序在某种意义上是通用的，它们可以应用于任何通用库的组合，其中可能包括傅立叶，截断多项式，样条和小波基。该方法还将半参数模型中的变量选择与基选择相结合。许多领域正在收集越来越复杂的数据集。强大的统计方法对于从数据中提取尽可能多的信息是必不可少的。计算能力的进步为建模者提供了前所未有的机会，利用非参数和半参数建模技术来开发可能的隐藏结构。本提案中开发的新方法构成了自适应非参数和半参数建模程序的进步。这些方法和软件非常通用，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、卫生和医学、物理科学和社会科学。拟议的活动包括为将来的统计研究人员培训研究生。私家侦探与环境、医学和社会科学领域的调查人员进行了若干合作。一些提出的方法将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，并将提交给综合R档案网络。

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.