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An asymptotically most Bias-Robust invariant estimator of location

Part of the Lecture Notes in Mathematics book series (LNM,volume 1233)

Abstract

Huber (1981) has shown that for symmetric and unimodal parent distribution function the asymptotically most bias-robust sequence of invariant estimators of the location parameter under ɛ-contamination is the sequence of sample medians. We show, without the assumption of symmetry, that X L(n):nC, n≥1, for X i:n being ith order statistic in the sample X 1, X 2, ..., X n and for properly chosen L(n) and C, is asymptotically most bias-robust sequence of estimators of location.

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References

  1. R.N. Bhattacharya, R. Ranga Rao: Normal Approximation and Asymptotic Expansions, J. Wiley (1976).

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© 1987 Springer-Verlag

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Rychlik, T., Zieliński, R. (1987). An asymptotically most Bias-Robust invariant estimator of location. In: Kalashnikov, V.V., Penkov, B., Zolotarev, V.M. (eds) Stability Problems for Stochastic Models. Lecture Notes in Mathematics, vol 1233. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0072721

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  • DOI: https://doi.org/10.1007/BFb0072721

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17204-8

  • Online ISBN: 978-3-540-47394-7

  • eBook Packages: Springer Book Archive