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On linear models with long memory and heavy-tailed errors

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  • Zhou, Zhou
  • Wu, Wei Biao

Abstract

We consider the robust estimation of regression parameters in linear models with long memory and heavy-tailed errors. Asymptotic Bahadur-type representations of robust estimates are developed and their limiting distributions are obtained. It is shown that the limiting distributions are very different from those obtained under short memory. A simulation study is carried out to compare the performance of various asymptotic representations.

Suggested Citation

  • Zhou, Zhou & Wu, Wei Biao, 2011. "On linear models with long memory and heavy-tailed errors," Journal of Multivariate Analysis, Elsevier, vol. 102(2), pages 349-362, February.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:2:p:349-362
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    References listed on IDEAS

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    1. Zeckhauser, Richard & Thompson, Mark, 1970. "Linear Regression with Non-Normal Error Terms," The Review of Economics and Statistics, MIT Press, vol. 52(3), pages 280-286, August.
    2. Koenker,Roger, 2005. "Quantile Regression," Cambridge Books, Cambridge University Press, number 9780521845731, September.
    3. Phillips, P.C.B., 1991. "A Shortcut to LAD Estimator Asymptotics," Econometric Theory, Cambridge University Press, vol. 7(4), pages 450-463, December.
    4. 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.
    5. Cui, Hengjian & He, Xuming & Ng, Kai W., 2004. "M-estimation for linear models with spatially-correlated errors," Statistics & Probability Letters, Elsevier, vol. 66(4), pages 383-393, March.
    6. 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.
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