Fast highly efficient and robust one-step \(M\)-estimators of scale based on \(Q_n\). (English) Zbl 1506.62169

Smirnov, Pavel O.; Shevlyakov, Georgy L.

Comput. Stat. Data Anal. 78, 153-158 (2014).

Summary: A parametric family of \(M\)-estimators of scale based on the Rousseeuw-Croux \(Q_n\)-estimator is proposed; estimator’s bias and efficiency are studied. A low-complexity one-step \(M\)-estimator is obtained allowing a considerably faster computation with greater than 80% efficiency and the highest possible 50% breakdown point. Analytical and Monte Carlo modeling results confirm the effectiveness of the proposed approach.

MSC:

62-08	Computational methods for problems pertaining to statistics
62F35	Robustness and adaptive procedures (parametric inference)

Keywords:

robustness; \(M\)-estimator; scale estimation; influence function

Software:

robcor; Find

References:

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