Adaptive Regression via Basis Selection from Multiple Libraries

University Of California-Santa Barbara, Santa Barbara CA

Investigators

Abstract

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.