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Large-Sample Inference for Nonparametric Regression with Dependent Errors - (Now published in 'Annals of Statistics', 28 (1997), pp.2054-2083.)

Author

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  • Peter M Robinson
Abstract
A 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.

Suggested Citation

  • Peter M Robinson, 1997. "Large-Sample Inference for Nonparametric Regression with Dependent Errors - (Now published in 'Annals of Statistics', 28 (1997), pp.2054-2083.)," STICERD - Econometrics Paper Series 336, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    • Handle: RePEc:cep:stiecm:336
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    Citations

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    Cited by:

    1. Robinson, Peter, 2008. "Inference on nonparametrically trending time series with fractional errors," LSE Research Online Documents on Economics 25471, London School of Economics and Political Science, LSE Library.
    2. Peter M Robinson, 2004. "ROBUST COVARIANCE MATRIX ESTIMATION: "HAC" Estimates with Long Memory/Antipersistence Correction," STICERD - Econometrics Paper Series 471, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    3. Robinson, Peter M., 2004. "Robust covariance matrix estimation : HAC estimates with long memory/antipersistence correction," LSE Research Online Documents on Economics 2157, London School of Economics and Political Science, LSE Library.
    4. Robinson, P.M., 2011. "Asymptotic theory for nonparametric regression with spatial data," Journal of Econometrics, Elsevier, vol. 165(1), pages 5-19.
    5. Peter M Robinson, 2009. "Developments in the Analysis of Spatial Data," STICERD - Econometrics Paper Series 531, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Peter M Robinson, 2009. "Inference On Nonparametrically Trending Time Series With Fractional Errors," STICERD - Econometrics Paper Series 532, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    7. Robinson, Peter, 2008. "Developments in the analysis of spatial data," LSE Research Online Documents on Economics 25473, London School of Economics and Political Science, LSE Library.

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