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On optimal B-robust influence functions in multidimensional parametric models. (English) Zbl 0825.62137

Summary: In this paper we consider robust estimation in multidimensional parametric models. Following Hampel’s approach we focus on estimates with bounded influence functions, and try to find the optimal B-robust influence functions that solve Hampel’s variational problem. We have established existence and uniqueness of the optimal influence functions with the form as stated by Hampel et al. (1986). The optimal influence functions are shown to be continuous with respect to the parameters. This property enables us to construct the corresponding optimal B-robust estimates using a one-step procedure.

MSC:

62-XX Statistics
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[1] DOI: 10.1214/aos/1176345863 · Zbl 0489.62033 · doi:10.1214/aos/1176345863
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