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Global robustness of location and dispersion estimates

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  • Berrendero, José R.
  • Zamar, Ruben H.

Abstract

We analyze the global robustness of location and dispersion estimates using the concept of relative explosion rate. The merits of several dispersion estimates are compared when the dispersion parameter itself is of main interest and also when they are auxiliary estimates needed to define scale equivariant location M-estimates. We have also compared location M-estimates and found that the choice of score function (its shape) is of secondary importance in comparison with the choice of the tuning constant and the auxiliary dispersion estimate. Finally, we use the explosion rate to assess the combined effect of the tuning constant and auxiliary dispersion estimate on the global robustness properties of location M-estimates.

Suggested Citation

  • Berrendero, José R. & Zamar, Ruben H., 1999. "Global robustness of location and dispersion estimates," Statistics & Probability Letters, Elsevier, vol. 44(1), pages 63-72, August.
    • Handle: RePEc:eee:stapro:v:44:y:1999:i:1:p:63-72
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    1. Rousseeuw, Peter J. & Croux, Christophe, 1994. "The bias of k-step M-estimators," Statistics & Probability Letters, Elsevier, vol. 20(5), pages 411-420, August.
    2. Berrendero Díaz, José Ramón & Zamar, Rubén, 1995. "On the maxbias curve of residual admissible robust regression estimates," DES - Working Papers. Statistics and Econometrics. WS 10349, Universidad Carlos III de Madrid. Departamento de Estadística.
    3. Hossjer, O. & Croux, C. & Rousseeuw, P. J., 1994. "Asymptotics of Generalized S-Estimators," Journal of Multivariate Analysis, Elsevier, vol. 51(1), pages 148-177, October.
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    Cited by:

    1. Fried, Roland H., 2003. "Robust filtering of time series with trends," Technical Reports 2003,30, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Marek Omelka & Matías Salibián-Barrera, 2010. "Uniform asymptotics for S- and MM-regression estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 62(5), pages 897-927, October.

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