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Asymptotic normality of regression estimators with long memory errors

Author

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  • Giraitis, Liudas
  • Koul, Hira L.
  • Surgailis, Donatas

Abstract

This paper discusses asymptotic normality of certain classes of M- and R-estimators of the slope parameter vector in linear regression models with long memory moving average errors, extending recent results of Koul (1992) and Koul and Mukherjee (1993). Like in the case of the long memory Gaussian errors, it is observed that all these estimators are asymptotically equivalent to the least squares estimator, a fact that is in sharp contrast with the i.i.d. errors case.

Suggested Citation

  • Giraitis, Liudas & Koul, Hira L. & Surgailis, Donatas, 1996. "Asymptotic normality of regression estimators with long memory errors," Statistics & Probability Letters, Elsevier, vol. 29(4), pages 317-335, September.
  • Handle: RePEc:eee:stapro:v:29:y:1996:i:4:p:317-335
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    References listed on IDEAS

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    1. Koul, Hira L., 1992. "M-estimators in linear models with long range dependent errors," Statistics & Probability Letters, Elsevier, vol. 14(2), pages 153-164, May.
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    Cited by:

    1. Beran, Jan & Feng, Yuanhua & Ghosh, Sucharita & Sibbertsen, Philipp, 2002. "On robust local polynomial estimation with long-memory errors," International Journal of Forecasting, Elsevier, vol. 18(2), pages 227-241.
    2. Li, Linyuan, 2003. "On Koul's minimum distance estimators in the regression models with long memory moving averages," Stochastic Processes and their Applications, Elsevier, vol. 105(2), pages 257-269, June.
    3. Hira Koul & Nao Mimoto & Donatas Surgailis, 2013. "Goodness-of-fit tests for long memory moving average marginal density," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(2), pages 205-224, February.
    4. Toshio Honda, 2010. "Nonparametric estimation of conditional medians for linear and related processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(6), pages 995-1021, December.
    5. Hira Koul & Donatas Surgailis & Nao Mimoto, 2015. "Minimum distance lack-of-fit tests under long memory errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 78(2), pages 119-143, February.
    6. Mohamed Boutahar, 2006. "Limiting distribution of the least squaresestimates in polynomial regression with longmemory noises," Working Papers halshs-00409571, HAL.
    7. Lihong Wang, 2004. "Asymptotics of estimates in constrained nonlinear regression with long-range dependent innovations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 56(2), pages 251-264, June.
    8. Beran, Jan, 2006. "On location estimation for LARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1766-1782, September.
    9. Youndjé, É. & Vieu, P., 2006. "A note on quantile estimation for long-range dependent stochastic processes," Statistics & Probability Letters, Elsevier, vol. 76(2), pages 109-116, January.
    10. Zhao, Zhibiao & Wu, Wei Biao, 2007. "Asymptotic theory for curve-crossing analysis," Stochastic Processes and their Applications, Elsevier, vol. 117(7), pages 862-877, July.
    11. Ould Haye, Mohamedou & Philippe, Anne, 2011. "Marginal density estimation for linear processes with cyclical long memory," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1354-1364, September.
    12. Koul, Hira L. & Surgailis, Donatas, 2001. "Asymptotics of empirical processes of long memory moving averages with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 91(2), pages 309-336, February.
    13. Comte, F. & Merlevède, F., 2005. "Super optimal rates for nonparametric density estimation via projection estimators," Stochastic Processes and their Applications, Elsevier, vol. 115(5), pages 797-826, May.
    14. Surgailis, Donatas, 0. "Stable limits of empirical processes of moving averages with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 100(1-2), pages 255-274, July.
    15. Hira L. Koul & Nao Mimoto & Donatas Surgailis, 2016. "A goodness-of-fit test for marginal distribution of linear random fields with long memory," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(2), pages 165-193, February.
    16. Hira Koul & Donatas Surgailis, 2000. "Asymptotic Normality of the Whittle Estimator in Linear Regression Models with Long Memory Errors," Statistical Inference for Stochastic Processes, Springer, vol. 3(1), pages 129-147, January.
    17. Tassos Magdalinos, 2008. "Mildly explosive autoregression under weak and strong dependence," Discussion Papers 08/05, University of Nottingham, Granger Centre for Time Series Econometrics.
    18. Toshio Honda, 2009. "Nonparametric density estimation for linear processes with infinite variance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(2), pages 413-439, June.
    19. Lorek, Paweł & Kulik, Rafał, 2014. "Empirical process of residuals for regression models with long memory errors," Statistics & Probability Letters, Elsevier, vol. 86(C), pages 7-16.
    20. Magdalinos, Tassos, 2012. "Mildly explosive autoregression under weak and strong dependence," Journal of Econometrics, Elsevier, vol. 169(2), pages 179-187.
    21. Koul, Hira L. & Baillie, Richard T., 2003. "Asymptotics of M-estimators in non-linear regression with long memory designs," Statistics & Probability Letters, Elsevier, vol. 61(3), pages 237-252, February.

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