Large-sample inference for nonparametric regression with dependent errors

Peter M. Robinson

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

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: Central limit theorem; nonparametric regression; autocorrelation; long range dependence. AMS 1991 subject classifications : Primary 62G07; 60G18; secondary 62G20. (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Date: 1997
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Citations: View citations in EconPapers (54)

Published in Annals of Statistics, 1997, 25(5), pp. 2054-2083. ISSN: 0090-5364

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