Regression-type inference in nonparametric autoregression

• 成果类型: Article
• 署名作者: Neumann, MH; Kreiss, JP
• 署名单位: Humboldt University of Berlin; Braunschweig University of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1998
• 页码: 1570-1613
• 关键词: CONFIDENCE BANDS; asymptotic equivalence; DENSITY-ESTIMATION; linear-regression; white-noise; time-series; CONVERGENCE; bandwidth

摘要

We derive a strong approximation of a local polynomial estimator (LPE) in nonparametric autoregression by an LPE in a corresponding nonparametric regression model. This generally suggests the application of regression-typical tools for statistical inference in nonparametric autoregressive models. It provides an important simplification for the bootstrap method to be used: It is enough to mimic the structure of a nonparametric regression model rather than to imitate the more complicated process structure in the autoregressive case. As an example we consider a simple wild bootstrap, which is used for the construction of simultaneous confidence bands and nonparametric supremum-type tests.