Least median of weighted squares in logistic regression with large strata. (English) Zbl 0807.62029
Summary: One aim of robust regression is to find estimators with high finite sample breakdown points. Although various robust estimators have been proposed in logistic regression models, their breakdown points are not yet known. Here it is shown for logistic regression models with binary data that there is no estimator with a high finite sample breakdown point, provided the estimator has to fulfill a weak condition. In logistic regression models with large strata however, a modification of P. J. Rousseeuw’s [J. Am. Stat. Assoc. 79, 871-880 (1984; Zbl 0547.62046)] least median of square estimator is shown to have a finite sample breakdown point of approximately \(1/2\).
MSC:
62F35 | Robustness and adaptive procedures (parametric inference) |
62J99 | Linear inference, regression |
62P10 | Applications of statistics to biology and medical sciences; meta analysis |