Asymptotic behavior for S-estimators in random design linear model with long-range-dependent errors

Abstract

The asymptotic behavior of S-estimators in a random design linear model with long-range-dependent Gaussian errors is considered. It turns out that the S-estimators of regression parameter and error variance are strongly consistent under mild conditions. Furthermore, the asymptotic distribution of the S-estimator of regression parameter is normal if the design vectors are i.i.d. and is non-normal if the design vectors are long-range dependent Gaussian vectors. We also show that the asymptotic distribution of S-estimator of the error variance is non-normal since the errors are long-range dependent.

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Correspondence to Li Degui.

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Supported by National Natural Science Foundation of China (Grant No. 10571159) and Specialized Research Fund for the Doctor Program of Higher Education (Grant No. 2002335090).

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Zhengyan, L., Degui, L. & Jia, C. Asymptotic behavior for S-estimators in random design linear model with long-range-dependent errors. Metrika 66, 289–303 (2007). https://doi.org/10.1007/s00184-006-0111-6

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Keywords

  • Asymptotic distribution
  • Consistency
  • Linear model
  • Long-range dependence
  • S-estimator