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Algorithms for bounded-influence estimation. (English) Zbl 1161.62322

Summary: Bounded-influence estimation is a well developed and useful theory. It provides fairly efficient estimators which are robust to outliers and local model departures. However, its use has been limited thus far, mainly because of computational difficulties. A careful implementation in modern statistical software can effectively overcome the numerical problems of bounded-influence estimators. The proposed approach is based on general methods for solving estimating equations, together with suitable methods developed in the statistical literature, such as the delta algorithm and nested iterations. The focus is on Mallows estimation in generalized linear models and on optimal bias-robust estimation in models for independent data, such as regression models with asymmetrically distributed errors.

MSC:

62F10 Point estimation
62J12 Generalized linear models (logistic models)
65C60 Computational problems in statistics (MSC2010)
62F35 Robustness and adaptive procedures (parametric inference)

Software:

sn; R; ROBETH; robGLM1; MASS (R)
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Full Text: DOI

References:

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