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Moderate and Cramer-type large deviation theorems for M-estimators

Author

Listed:
  • Jurecková, J.
  • Kallenberg, W. C. M.
  • Veraverbeke, N.

Abstract

The known central limit result for broad classes of M-estimators is refined to moderate and large deviation behaviour. The results are applied in relating the local inaccuracy rate and the asymptotic variance of M-estimators in the location and scale problem.

Suggested Citation

  • Jurecková, J. & Kallenberg, W. C. M. & Veraverbeke, N., 1988. "Moderate and Cramer-type large deviation theorems for M-estimators," Statistics & Probability Letters, Elsevier, vol. 6(3), pages 191-199, February.
    • Handle: RePEc:eee:stapro:v:6:y:1988:i:3:p:191-199
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    Cited by:

    1. Ermakov Mikhail, 2007. "Importance sampling for simulations of moderate deviation probabilities of statistics," Statistics & Risk Modeling, De Gruyter, vol. 25(4/2007), pages 1-20, October.
    2. Christis Katsouris, 2022. "Asymptotic Theory for Unit Root Moderate Deviations in Quantile Autoregressions and Predictive Regressions," Papers 2204.02073, arXiv.org, revised Aug 2023.
    3. Bai, Yansong & Zhang, Yong & Liu, Congmin, 2023. "Moderate deviation principle for likelihood ratio test in multivariate linear regression model," Journal of Multivariate Analysis, Elsevier, vol. 194(C).
    4. Jiang, Hui & Wang, Shaochen, 2017. "Moderate deviation principles for classical likelihood ratio tests of high-dimensional normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 156(C), pages 57-69.

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