Large-Sample Inference for Nonparametric Regression with Dependent Errors - (Now published in 'Annals of Statistics', 28 (1997), pp.2054-2083.)
AbstractA central limit theorem is given for certain weighted 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 behaviour 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 regime pertains, and show also that a simpler studentization is possible when long-range dependence can be taken for granted.
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Bibliographic InfoPaper provided by Suntory and Toyota International Centres for Economics and Related Disciplines, LSE in its series STICERD - Econometrics Paper Series with number /1997/336.
Date of creation: Sep 1997
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Web page: http://sticerd.lse.ac.uk/_new/publications/default.asp
central limit theorem; nonparametric regression; autocorrelation; long-range dependence;
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