Summary
The change-of-variance function is defined for estimators of regression coefficients. Both an unstandardized and a standardized form of the change-of-variance sensitivity are introduced, and their relation with the corresponding gross-error-sensitivities is investigated. The problems of optimal robustness lead to the Hampel-Krasker and the Krasker-Welsch estimators. At the same time, also the scale parameter has to be estimated robustly. By means of the change-of-variance sensitivity, optimal robust redescending scale estimators are constructed.
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Ronchetti, E., Rousseeuw, P.J. Change-of-variance sensitivities in regression analysis. Z. Wahrscheinlichkeitstheorie verw Gebiete 68, 503–519 (1985). https://doi.org/10.1007/BF00535342
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DOI: https://doi.org/10.1007/BF00535342