The Annals of Statistics
- Ann. Statist.
- Volume 25, Number 5 (1997), 2054-2083.
Large-sample inference for nonparametric regression with dependent errors
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.
Ann. Statist., Volume 25, Number 5 (1997), 2054-2083.
First available in Project Euclid: 20 November 2003
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Robinson, P. M. Large-sample inference for nonparametric regression with dependent errors. Ann. Statist. 25 (1997), no. 5, 2054--2083. doi:10.1214/aos/1069362387. https://projecteuclid.org/euclid.aos/1069362387