Large-sample inference for nonparametric regression with dependent errors
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.
|Date of creation:||1997|
|Publication status:||Published in Annals of Statistics, 1997, 25(5), pp. 2054-2083. ISSN: 0090-5364|
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- Roussas, George G. & Tran, Lanh T. & Ioannides, D. A., 1992. "Fixed design regression for time series: Asymptotic normality," Journal of Multivariate Analysis, Elsevier, vol. 40(2), pages 262-291, February.
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- Robinson, P M, 1993. "Highly Insignificant F-Ratios," Econometrica, Econometric Society, vol. 61(3), pages 687-696, May.
- Andrew Harvey (ed.), 1994. "Time Series," Books, Edward Elgar Publishing, volume 0, number 599.
- Deo, R. S., 1997. "Nonparametric regression with long-memory errors," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 89-94, April.
- Hall, Peter & Hart, Jeffrey D., 1990. "Nonparametric regression with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 36(2), pages 339-351, December.
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