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October 1997 Large-sample inference for nonparametric regression with dependent errors
P. M. Robinson
Ann. Statist. 25(5): 2054-2083 (October 1997). DOI: 10.1214/aos/1069362387


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.


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P. M. Robinson. "Large-sample inference for nonparametric regression with dependent errors." Ann. Statist. 25 (5) 2054 - 2083, October 1997.


Published: October 1997
First available in Project Euclid: 20 November 2003

zbMATH: 0882.62039
MathSciNet: MR1474083
Digital Object Identifier: 10.1214/aos/1069362387

Primary: 60G18 , 62G07
Secondary: 62G20

Keywords: Autocorrelation , central limit theorem , Long range dependence , Nonparametric regression

Rights: Copyright © 1997 Institute of Mathematical Statistics


Vol.25 • No. 5 • October 1997
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