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):n−C, 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.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
R.N. Bhattacharya, R. Ranga Rao: Normal Approximation and Asymptotic Expansions, J. Wiley (1976).
D. Feldman, H.G. Tucker: Estimation of Non-unique Quantities. Ann. Math. Statist. (1966), 37, 451–457.
P.J. Huber: Robust Statistics. J. Wiley (1981).
R. Zieliński: Robust statistical procedures: a general approach. In: Stability Problems for Stochastic Models (Ed. V.V. Kalashnikov and V.M. Zolotarev). Lecture Notes in Mathematics 982 (1983), Springer-Verlag.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1987 Springer-Verlag
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/BFb0072721
Received:
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-17204-8
Online ISBN: 978-3-540-47394-7
eBook Packages: Springer Book Archive
