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Breakdown point of Schuster-Narvarte's location estimator

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  • Chen, Zhiqiang

Abstract

The Schuster-Narvarte's (Ann. Statist. 1 (1973) 1096-1104) location parameter of a distribution F, the center of a symmetric distribution closest to F, is an appealing definition for the center of distributions. It is noticed that this parameter is a special case of Donoho and Liu's (Ann. Statist. 16 (1988) 552-586) semiparametric minimum distance functional. For this estimator, an algorithm is available in Schuster-Narvarte (1973); asymptotics results were established in Rao et al. (Ann. Statist. 3 (1975) 862-873) and in Arcones and Giné (Ann. Statist. 19 (1991) 1496-1511); validity of bootstraps is proved in Arcones and Giné (1991) while simulation results can be found in Schuster and Barker (Comm. Statist. Simulation Comput. 16 (1987) 69-84). In this article, we compliment the study by establishing the robustness properties for the Schuster-Narvarte's estimator. A general result for the (enlargement) finite sample breakdown point is established. In particular, when the underlying distribution is symmetric, the limiting finite sample breakdown point is almost surely .

Suggested Citation

  • Chen, Zhiqiang, 2000. "Breakdown point of Schuster-Narvarte's location estimator," Statistics & Probability Letters, Elsevier, vol. 48(3), pages 283-286, July.
    • Handle: RePEc:eee:stapro:v:48:y:2000:i:3:p:283-286
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