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Asymptotic distribution of linear unbiased estimators in the presence of heavy-tailed stochastic regressors and residuals

Author

Listed:
  • Samorodnitsky, Gennady
  • Rachev, Svetlozar T.
  • Kurz-Kim, Jeong-Ryeol

Abstract

Under the symmetric α-stable distributional assumption for the disturbances, Blattberg et al (1971) consider unbiased linear estimators for a regression model with non-stochastic regressors. We consider both the rate of convergence to the true value and the asymptotic distribution of the normalized error of the linear unbiased estimators. By doing this, we allow the regressors to be stochastic and disturbances to be heavy-tailed with either finite or infinite variances, where the tail-thickness parameters of the regressors and disturbances may be different.

Suggested Citation

  • Samorodnitsky, Gennady & Rachev, Svetlozar T. & Kurz-Kim, Jeong-Ryeol, 2005. "Asymptotic distribution of linear unbiased estimators in the presence of heavy-tailed stochastic regressors and residuals," Discussion Paper Series 1: Economic Studies 2005,21, Deutsche Bundesbank.
    • Handle: RePEc:zbw:bubdp1:4215
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    References listed on IDEAS

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    1. Falko Fecht & Kevin X. D. Huang & Antoine Martin, 2008. "Financial Intermediaries, Markets, and Growth," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 40(4), pages 701-720, June.
    2. Hamburg, Britta & Hoffmann, Mathias & Keller, Joachim, 2005. "Consumption, wealth and business cycles: why is Germany different?," Discussion Paper Series 1: Economic Studies 2005,16, Deutsche Bundesbank.
    3. Britta Hamburg & Mathias Hoffmann & Joachim Keller, 2008. "Consumption, wealth and business cycles in Germany," Empirical Economics, Springer, vol. 34(3), pages 451-476, June.
    4. Hamerle, Alfred & Liebig, Thilo & Scheule, Harald, 2004. "Forecasting Credit Portfolio Risk," Discussion Paper Series 2: Banking and Financial Studies 2004,01, Deutsche Bundesbank.
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    Cited by:

    1. Ortobelli, Sergio & Rachev, Svetlozar T. & Fabozzi, Frank J., 2010. "Risk management and dynamic portfolio selection with stable Paretian distributions," Journal of Empirical Finance, Elsevier, vol. 17(2), pages 195-211, March.

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    Keywords

    Asymptotic distribution; rate of convergence; stochastic regressor; stable non-Gaussian; finite or infinite variance; heavy tails;
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