Large-sample inference for nonparametric regression with dependent errors

• 成果类型: Article
• 署名作者: Robinson, PM
• 署名单位: University of London; London School Economics & Political Science
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1069362387
• 发表日期: 1997
• 页码: 2054-2083
• 关键词: long-range dependence; fixed-design regression; time-series; CONVERGENCE; parameter; bandwidth

摘要

A central limit theorem is given for certain weighted partial sums of a covariance stationary process, assuming it is linear in martingale differences, but without any restriction on its spectrum. We apply the result to kernel nonparametric fixed-design regression, giving a single central limit theorem which indicates how error spectral behavior at only zero frequency influences the asymptotic distribution and covers long-range, short-range and negative dependence. We show how the regression estimates can be Studentized in the absence of previous knowledge of which form of dependence pertains, and show also that a simpler Studentization is possible when long-range dependence can be taken for granted.