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June, 1988 The Length of the Shorth
R. Grubel
Ann. Statist. 16(2): 619-628 (June, 1988). DOI: 10.1214/aos/1176350823

Abstract

Let $\hat{H}_n(\alpha) (0 < \alpha < 1)$ denote the length of the shortest $\alpha$-fraction of the ordered sample $X_{1:n}, X_{2:n}, \cdots, X_{n:n}$, i.e., $\hat{H}_n(\alpha) = \min\{X_{k + j:n} - X_{k:n}: 1 \leq k \leq k + j \leq n; (j + 1)/n \geq \alpha\}.$ Such quantities arise in the context of robust scale estimation. Using the concept of compact derivatives of statistical functionals, the asymptotic behaviour of $\hat{H}_n(\alpha)$ as $n \rightarrow \infty$ is investigated.

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R. Grubel. "The Length of the Shorth." Ann. Statist. 16 (2) 619 - 628, June, 1988. https://doi.org/10.1214/aos/1176350823

Information

Published: June, 1988
First available in Project Euclid: 12 April 2007

zbMATH: 0664.62040
MathSciNet: MR947565
Digital Object Identifier: 10.1214/aos/1176350823

Subjects:
Primary: 62G05
Secondary: 60F17, 62E20, 62F35

Rights: Copyright © 1988 Institute of Mathematical Statistics

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Vol.16 • No. 2 • June, 1988
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