One-step robust parametric estimation with application to random censoring model
For robust parametric estimation Beran (1982) derived local minimum distance functionals and constructed one-step estimators for them that are asymptotically minimax robust. For some distances the efficiency of Beran's estimators may not be very high. There are also some difficulties in directly imitating Beran's argument for the random censoring model. In this paper we represent Beran's functionals as the one-step M-estimation functional of Hampel (1968) and Huber (1981) for a proper score function. This suggests that one can directly work with the score function, which can be chosen to have any prescribed level of efficiency at the model. Also, the representation suggests a proper form of the local functionals in the random censoring model. Asymptotically minimax robust estimators of these functionals are constructed using the one-step method. The proofs rely on Beran (1982).
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Volume (Year): 26 (1996)
Issue (Month): 3 (February)
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