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Large-sample inference for nonparametric regression with dependent errors

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  • Robinson, Peter M.

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.

Suggested Citation

  • Robinson, Peter M., 1997. "Large-sample inference for nonparametric regression with dependent errors," LSE Research Online Documents on Economics 302, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:302
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    File URL: http://eprints.lse.ac.uk/302/
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    References listed on IDEAS

    as
    1. Csörgo, Sándor & Mielniczuk, Jan, 1995. "Distant long-range dependent sums and regression estimation," Stochastic Processes and their Applications, Elsevier, vol. 59(1), pages 143-155, September.
    2. Andrew Harvey (ed.), 1994. "Time Series," Books, Edward Elgar Publishing, volume 0, number 599, June.
    3. 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.
    4. 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.
    5. Robinson, P M, 1993. "Highly Insignificant F-Ratios," Econometrica, Econometric Society, vol. 61(3), pages 687-696, May.
    6. Deo, R. S., 1997. "Nonparametric regression with long-memory errors," Statistics & Probability Letters, Elsevier, vol. 33(1), pages 89-94, April.
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    More about this item

    Keywords

    Central limit theorem; nonparametric regression; autocorrelation; long range dependence. AMS 1991 subject classifications : Primary 62G07; 60G18; secondary 62G20.;

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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