k-step versions Mn (k) of studentized M-estimator Mn of location generated by various types of score functions are studied. The rate of approximation of Mn by Mn (k) (n → ∞, k fixed) is derived with the aid of the uniform asymptotic linearity results of three-parameters empirical M-processes. While the rate is considerably improved with increasing k for absolutely continuous score functions, it is improved very slowly for functions with jump-discontinuities where it can never be better than Op(n-1).
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Jurečková et al. (1995) studied this question.
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