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Asymptotic normality of multivariate trimmed means

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  • Arcones, Miguel A.

Abstract

We prove the asymptotic normality of the trimmed mean, obtained by deleting the data which is further away from a parameter of location [theta]n. To get this trimmed mean, equivariant by rotations, dilations and translations, we choose [theta]n in a class of multivariate parameters of location, which are equivariant by these transformations. Given the data X1, ... , Xn, we take as [theta]n, the value such that where h is a nondecreasing function and x is the Euclidean distance in Bd. This estimator [theta]n is equivariant by rotations and translations. If h(x) = xp, [theta]n is also equivariant by dilations.

Suggested Citation

  • Arcones, Miguel A., 1995. "Asymptotic normality of multivariate trimmed means," Statistics & Probability Letters, Elsevier, vol. 25(1), pages 43-53, October.
    • Handle: RePEc:eee:stapro:v:25:y:1995:i:1:p:43-53
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    References listed on IDEAS

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    1. Nolan, D., 1992. "Asymptotics for multivariate trimming," Stochastic Processes and their Applications, Elsevier, vol. 42(1), pages 157-169, August.
    2. Arcones, Miguel A., 1996. "Some remarks on the uniform weak convergence of stochastic processes," Statistics & Probability Letters, Elsevier, vol. 28(1), pages 41-49, June.
    3. Arcones, Miguel A., 1994. "Distributional convergence of M-estimators under unusual rates," Statistics & Probability Letters, Elsevier, vol. 21(4), pages 271-280, November.
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    Cited by:

    1. Miguel Arcones, 1998. "The Bahadur-Kiefer Representation of the Two Dimensional Spatial Medians," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(1), pages 71-86, March.
    2. Olive, David J., 2004. "A resistant estimator of multivariate location and dispersion," Computational Statistics & Data Analysis, Elsevier, vol. 46(1), pages 93-102, May.

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