Summary
The infinitesimal stability of the asymptotic variance is considered forM-estimators of a location parameter when the nominal sample with i.i.d. data is contaminated by a possibly dependent process. It is shown that the resulting change-of-variance function can be expressed as a sum of two terms, one corresponding contamination of the univariate distribution, and one to contamination of the bivariate distributions. A change-of-variance sensitivity is introduced, the form of which is closely related to the average patch length of the outliers. Finally, optimalV-robust and mostV-robust score functions are derived. The resulting family of estimators is the same as for independent data in the general case, but the truncation point approaches zero when dependency is accounted for. For redescending score-functions, the family of estimators is changed.
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This paper was written under support by the Swedish Board for Technical Development, contract 712-89-1073
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Hössjer, O. The change-of-variance function for dependent data. Probab. Th. Rel. Fields 90, 447–467 (1991). https://doi.org/10.1007/BF01192138
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DOI: https://doi.org/10.1007/BF01192138