On the maximum bias functions of MM-estimates and constrained M-estimates of regression
| Autor: | José R. Berrendero, David E. Tyler, Beatriz V. M. Mendes |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2007 |
| Předmět: |
Statistics and Probability
Mathematics - Statistics Theory Statistics Theory (math.ST) Function (mathematics) Estadística Regression maximum bias curves symbols.namesake S-estimates breakdown point constrained M-estimates 62J05 FOS: Mathematics symbols Applied mathematics Statistics Probability and Uncertainty 62F35 (Primary) 62J05 (Secondary) Robust regression Gaussian network model 62F35 Mathematics M-estimates gross error sensitivity |
| Zdroj: | Ann. Statist. 35, no. 1 (2007), 13-40 Biblos-e Archivo. Repositorio Institucional de la UAM instname |
| Popis: | We derive the maximum bias functions of the MM-estimates and the constrained M-estimates or CM-estimates of regression and compare them to the maximum bias functions of the S-estimates and the $\tau$-estimates of regression. In these comparisons, the CM-estimates tend to exhibit the most favorable bias-robustness properties. Also, under the Gaussian model, it is shown how one can construct a CM-estimate which has a smaller maximum bias function than a given S-estimate, that is, the resulting CM-estimate dominates the S-estimate in terms of maxbias and, at the same time, is considerably more efficient. Comment: Published at http://dx.doi.org/10.1214/009053606000000975 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | OpenAIRE |
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