Norm restricted maximum likelihood estimators for binary regression models with parametric link

Parametric link transformation families have shown to be useful in the analysis of binary regression data since they avoid the problem of link misspecifaction. Inference for these models are commonly based on likelihood methods. Duffy and Santner (1988, 1989) however showed that ordinary logistic maximum likelihood estimators (MLE) have poor mean square error (MSE) behavior in small samples compared to alternative norm restricted estimators. This paper extends these alternative norm restricted estimators to binary regression models with any specified parametric link family. These extended norm restricted MLE’s are strongly consistent and efficient under regularity conditions. Finally a simulation study shows that an empiric version of norm restricted MLE’s exhibit superior MSE behavior in small samples compared to MLE’s with fixed known link.