Smoothing spline nonlinear nonparametric regression models

• 成果类型: Article
• 署名作者: Ke, CL; Wang, YD
• 署名单位: University of California System; University of California Santa Barbara
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1198/016214504000000755
• 发表日期: 2004
• 页码: 1166-1175
• 关键词: mixed-effects models; rate term structure; inference; algorithm

摘要

Almost all of the current nonparametric regression methods, such as smoothing splines, generalized additive models, and varying-coefficients models, assume a linear relationship when nonparametric functions are regarded as parameters. In this article we propose a general class of smoothing spline nonlinear nonparametric models that allow nonparametric functions to act nonlinearly. They arise in many fields as either theoretical or empirical models. Our new estimation methods are based on an extension of the, Gauss-Newton method to infinite-dimensional spaces and the backfitting procedure. We extend the generalized cross-validation and generalized maximum likelihood methods to estimate smoothing parameters. We establish connections between some nonlinear nonparametric models and nonlinear mixed-effects models. We derive approximate Bayesian confidence intervals for inference, We illustrate the methods with an application to term structure of interest rates and conduct simulations to evaluate the finite-sample performance of our methods.