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On optimal B-robust influence functions in semiparametric models. (English) Zbl 0844.62036
Summary: Bounded influence functions are used for robust estimation in semiparametric models. We generalize F. R. Hampel’s [Contributions to the theory of robust estimation. Ph.D. diss., Univ. Calif./Berkeley (1968)] variational problem to semiparametric models and define the optimal \(B\)-robust influence function as the one solving the variational problem. We identify the lowest bounds for influence functions and establish the existence and uniqueness of the optimal influence functions in general semiparametric models. Explicit optimal influence functions are given for a special case. Examples are provided to illustrate the procedures for calculating the optimal influence functions and for constructing the corresponding optimal estimators.

MSC:
62G35 Nonparametric robustness
62F35 Robustness and adaptive procedures (parametric inference)
49N99 Miscellaneous topics in calculus of variations and optimal control
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