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The least trimmed squares. I: Consistency. (English) Zbl 1248.62033

Summary: The consistency of the least trimmed squares estimator [see P.J. Rousseeuw, J. Am. Stat. Assoc. 79, 871–880 (1984; Zbl 0547.62046); or F.R. Hampel et al., Robust statistics. The approach based on influence functions. NY etc.: Wiley and Sons (1986; Zbl 0593.62027)] is proved under general conditions. The assumptions employed in this paper are discussed in detail to clarify the consequences for applications.

MSC:

62F12 Asymptotic properties of parametric estimators
62J05 Linear regression; mixed models
62F35 Robustness and adaptive procedures (parametric inference)
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