Maximum Bias Curves for Robust Regression with Non-elliptical Regressors
Berrendero, José ; Zamar, Ruben H.
Ann. Statist., Tome 29 (2001) no. 2, p. 224-251 / Harvested from Project Euclid
Maximum bias curves for some regression estimates were previously derived assuming that (i) the intercept term is known and/or (ii) the regressors have an elliptical distribution. We present a single method to obtain the maximum bias curves for a large class of regression estimates. Our results are derived under very mild conditions and, in particular, do not require the restrictive assumptions (i) and (ii) above. Using these results it is shown that the maximum bias curves heavily depend on the shape of the regressors' distribution which we call the x-configuration. Despite this big effect, the relative performance of different estimates remains unchanged under different x-configurations. We also explore the links between maxbias curves and bias bounds. Finally, we compare the robustness properties of some estimates for the intercept parameter.
Publié le : 2001-02-14
Classification:  robust regression,  maxbias curve,  S-estimates,  \tao-estimates,  R-estimates,  62F35
@article{996986507,
     author = {Berrendero, Jos\'e and Zamar, Ruben H.},
     title = {Maximum Bias Curves for Robust Regression with Non-elliptical Regressors},
     journal = {Ann. Statist.},
     volume = {29},
     number = {2},
     year = {2001},
     pages = { 224-251},
     language = {en},
     url = {http://dml.mathdoc.fr/item/996986507}
}
Berrendero, José; Zamar, Ruben H. Maximum Bias Curves for Robust Regression with Non-elliptical Regressors. Ann. Statist., Tome 29 (2001) no. 2, pp.  224-251. http://gdmltest.u-ga.fr/item/996986507/