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Robust estimation of the location of a vertical tangent in distribution. (English) Zbl 0862.62027

Summary: It is shown that the location of the set of \(m+1\) observations with minimal diameter, within local data, is a robust estimator of the location of a vertical tangent in a distribution function. The rate of consistency of these estimators is shown to be the same as that of asymptotically efficient estimators for the same model.
Robustness means (1) only properties of the distribution local to the vertical tangent play a role in the asymptotics, and (2) these asymptotics can be proven given approximate information about just two parameters, the shape and quantile of the vertical tangent.

MSC:

62F12 Asymptotic properties of parametric estimators
62F35 Robustness and adaptive procedures (parametric inference)
62E20 Asymptotic distribution theory in statistics
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[1] CHERNOFF, H. and RUBIN, H. 1956. The estimation of the location discontinuity in density. Proc. Third Berkeley Sy mp. Statist. Probab. 1 19 37. Univ. California Press, Berkeley. · Zbl 0072.36302
[2] FEDERER, H. 1969. Geometric Measure Theory. Springer, New York. · Zbl 0176.00801
[3] FELLER, W. 1971. An Introduction to Probability Theory and Its Applications, 2nd ed. Wiley, New York. · Zbl 0219.60003
[4] HALL, P. 1982. On estimating the endpoint of a distribution. Ann. Statist. 10 556 568. · Zbl 0489.62029
[5] IBRAGIMOV, I. A. and HAS’MINSKII, R. Z. 1981. Statistical Estimation Asy mptotic Theory Z. translated by Samuel Kotz. Springer, New York.
[6] STOUT, W. 1974. Almost Sure Convergence. Academic Press, New York. · Zbl 0321.60022
[7] EAST LANSING, MICHIGAN 48824
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