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Asymptotic normality of regression estimators with long memory errors


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


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.

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Bibliographic Info

Article provided by Elsevier in its journal Statistics & Probability Letters.

Volume (Year): 29 (1996)
Issue (Month): 4 (September)
Pages: 317-335

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Handle: RePEc:eee:stapro:v:29:y:1996:i:4:p:317-335

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Keywords: M-; R-estimators Appell polynomials Weighted empiricals;


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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. 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.
  2. Beran, Jan, 2006. "On location estimation for LARCH processes," Journal of Multivariate Analysis, Elsevier, vol. 97(8), pages 1766-1782, September.
  3. Hira Koul & Nao Mimoto & Donatas Surgailis, 2013. "Goodness-of-fit tests for long memory moving average marginal density," Metrika, Springer, vol. 76(2), pages 205-224, February.
  4. Toshio Honda, 2009. "Nonparametric density estimation for linear processes with infinite variance," Annals of the Institute of Statistical Mathematics, Springer, vol. 61(2), pages 413-439, June.
  5. Lihong Wang, 2004. "Asymptotics of estimates in constrained nonlinear regression with long-range dependent innovations," Annals of the Institute of Statistical Mathematics, Springer, vol. 56(2), pages 251-264, June.
  6. Beran, Jan & Feng, Yuanhua & Ghosh, Sucharita & Sibbertsen, Philipp, 2000. "On robust local polynominal estimation with long-memory errors," Technical Reports 2000,35, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
  7. 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.
  8. 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.
  9. Magdalinos, Tassos, 2012. "Mildly explosive autoregression under weak and strong dependence," Journal of Econometrics, Elsevier, vol. 169(2), pages 179-187.
  10. 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.
  11. Honda, Toshio, 2007. "Nonparametric Estimation of Conditional Medians for Linear and Related Processes," Discussion Papers 2005-04, Graduate School of Economics, Hitotsubashi University.
  12. 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.
  13. Mohamed Boutahar, 2006. "Limiting distribution of the least squaresestimates in polynomial regression with longmemory noises," Working Papers halshs-00409571, HAL.
  14. 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.
  15. Tassos Magdalinos, 2008. "Mildly explosive autoregression under weak and strong dependence," Discussion Papers 08/05, University of Nottingham, Granger Centre for Time Series Econometrics.
  16. 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.
  17. 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.
  18. 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.


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