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Tail behavior of the least-squares estimator

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  • Jurecková, Jana
  • Koenker, Roger
  • Portnoy, Stephen

Abstract

The tail behavior of the least-squares estimator in the linear regression model was studied in He et al. (Econometrica 58 (1990) 1195) under a fixed design for finite n. We now consider a random design matrix Xn and the case n-->[infinity] and study the probability with [gamma]n=F-1(1-1/n), a population analog of the maximal error. Unlike in the situation with fixed n and [gamma]-->[infinity], for n-->[infinity] we find fairly good tail behavior of LSE for normal F, for both fixed and random designs, even under heavy-tailed distribution for Xn.

Suggested Citation

  • Jurecková, Jana & Koenker, Roger & Portnoy, Stephen, 2001. "Tail behavior of the least-squares estimator," Statistics & Probability Letters, Elsevier, vol. 55(4), pages 377-384, December.
  • Handle: RePEc:eee:stapro:v:55:y:2001:i:4:p:377-384
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    References listed on IDEAS

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    1. He, Xuming, et al, 1990. "Tail Behavior of Regression Estimators and Their Breakdown Points," Econometrica, Econometric Society, vol. 58(5), pages 1195-1214, September.
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    Cited by:

    1. Jana Jurecková, 2003. "Statistical tests on tail index of a probability distribution," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(2), pages 151-190.
    2. Mikosch, Thomas & de Vries, Casper G., 2013. "Heavy tails of OLS," Journal of Econometrics, Elsevier, vol. 172(2), pages 205-221.
    3. Vijverberg, Wim P. & Hasebe, Takuya, 2015. "GTL Regression: A Linear Model with Skewed and Thick-Tailed Disturbances," IZA Discussion Papers 8898, Institute for the Study of Labor (IZA).

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