The author of this article introduces adaptive weighted maximum likelihood estimators for binary regression models. The asymptotic distribution under the model is established, and asymptotic confidence intervals are derived. Finite sample properties are studied by simulation. For clean datasets, the proposed adaptive estimators are more efficient than the nonadaptive ones even for moderate sample sizes, and for outlier contaminated datasets, they show a comparable robustness. As for the asymptotic confidence intervals, the actual coverage levels under the model are very close to the nominal levels (even for moderate sample sizes), and they are reasonbly stable under contamination. Binary regression models are very common in statistical applications. They are used in situations where a dochotomous response variable y_i and a vector of covariates x_i, are observed for each individual. The maximum likelihood estimator attains the minimum asymptotic variance under the model and then it is optimal, but it is very sensitive to a typical data. Observations with extreme covariates, in particular, have a large influence on the estimator, and if they are accompanied by misclassified responses, the resulting estimtates can be seriously biased. All these estimators differ greatly in terms of outli'er resistance and efficiency under the model. The authors have studied asymptotic and finite sample behavior of some of these estimators and found, for example, that suitably tuned Mallows-type estimators, (Carroll and Pederson (Ref. 1)) are very robust to outlier contamination, but inefficient under the model, which Schweppe-type estimators (Kunsch, et al. (Ref. 2)) are very efficient under the model, but show a poor outlier resistance. Although a trade-off between robustness and efficiency is inevitable, in this article the authors propose estimators that can be robust as Mallows-type estimators under contamination, but are much more efficient under the model (in fact, 100 percent efficient in some situations). This is achieved by an adaptive weighting scheme similar to that of Gervini (Refs. 3, The new adaptive estimators are introduced in Section 3, after a brief revision of some existing estimators. Their asymptotic distribution is established in Section 4 and asymptotic confidence ellipsoids are derived. Finite sample properties are studied in Section 6 by simulation. (16 refs.)
展开▼
