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Bounded Estimation in the Presence of Nuisance Parameters

Author

Listed:
  • Luca Greco

    (Department of Statistics)

  • Laura Ventura

    (Department of Statistics)

Abstract

The aim of this paper is to extend in a natural fashion the results on the treatment of nuisance parameters from the profile likelihood theory to the field of robust statistics. Similarly to what happens when there are no nuisance parameters, the attempt is to derive a bounded estimating function for a parameter of interest in the presence of nuisance parameters. The proposed method is based on a classical truncation argument of the theory of robustness applied to a generalized profile score function. By means of comparative studies, we show that this robust procedure for inference in the presence of a nuisance parameter can be used successfully in a parametric setting.

Suggested Citation

  • Luca Greco & Laura Ventura, 2006. "Bounded Estimation in the Presence of Nuisance Parameters," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 15(1), pages 27-36, May.
    • Handle: RePEc:spr:stmapp:v:15:y:2006:i:1:d:10.1007_s10260-006-0001-0
    DOI: 10.1007/s10260-006-0001-0
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    References listed on IDEAS

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    1. Butler, Richard J, et al, 1990. "Robust and Partially Adaptive Estimation of Regression Models," The Review of Economics and Statistics, MIT Press, vol. 72(2), pages 321-327, May.
    2. Ke-Hai Yuan & Robert Jennrich, 2000. "Estimating Equations with Nuisance Parameters: Theory and Applications," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 52(2), pages 343-350, June.
    3. Stefanski L. A. & Boos D. D., 2002. "The Calculus of M-Estimation," The American Statistician, American Statistical Association, vol. 56, pages 29-38, February.
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