The Annals of Statistics

Large-sample inference for nonparametric regression with dependent errors

P. M. Robinson

Full-text: Open access

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.

Article information

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

Dates
First available in Project Euclid: 20 November 2003

Permanent link to this document
https://projecteuclid.org/euclid.aos/1069362387

Digital Object Identifier
doi:10.1214/aos/1069362387

Mathematical Reviews number (MathSciNet)
MR1474083

Zentralblatt MATH identifier
0882.62039

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

Keywords
Central limit theorem nonparametric regression autocorrelation long range dependence

Citation

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


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