Large-sample inference for nonparametric regression with dependent errors
The Annals of Statistics · 1997 · Volume 25 · Issue 5
Abstract
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.
Keywords
60G18, 62G07, 62G20, Autocorrelation, central limit theorem, Long range dependence, Nonparametric regression
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