On the diversity of estimates. (English) Zbl 1052.62509

Summary: The presented examples of regression analysis of some real data sets below confirm that it is possible that various estimators may produce considerably different estimates. Such situation will be called diversity of estimates. Employing high breakdown point estimators, namely the least median of squares (LMS) and the least trimmed squares (LTS), the diversity of estimates is demonstrated. Two examples with the artificial data and a formal reflection of the diversity of estimates hint why the diversity of estimates takes place. The theoretical reflection also shows that the diversity of estimates may appear for any sample size. A proposal an how to select from the diverse estimates of model is given and illustrated in examples of real data sets.


62F10 Point estimation
62F99 Parametric inference
62F35 Robustness and adaptive procedures (parametric inference)
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