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Large-sample inference for nonparametric regression with dependent errors

Robinson, Peter M. (1997) Large-sample inference for nonparametric regression with dependent errors. Annals of Statistics, 25 (5). pp. 2054-2083. ISSN 0090-5364

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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.

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Additional Information: Published 1997 © Institute of Mathematical Statistics. LSE has developed LSE Research Online so that users may access research output of the School. Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Users may download and/or print one copy of any article(s) in LSE Research Online to facilitate their private study or for non-commercial research. You may not engage in further distribution of the material or use it for any profit-making activities or any commercial gain. You may freely distribute the URL ( of the LSE Research Online website.
Library of Congress subject classification: H Social Sciences > HA Statistics
Sets: Collections > Economists Online
Departments > Economics
Date Deposited: 15 Feb 2008

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