The Annals of Statistics

Large-sample inference for nonparametric regression with dependent errors

P. M. Robinson

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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.

Article information

Ann. Statist., Volume 25, Number 5 (1997), 2054-2083.

First available in Project Euclid: 20 November 2003

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation 60G18: Self-similar processes
Secondary: 62G20: Asymptotic properties

Central limit theorem nonparametric regression autocorrelation long range dependence


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.

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