This paper presents maximum score type estimators for linear, binomial, tobit and truncated regression models. These estimators estimate the normalized vector of slopes and do not provide the estimator of intercept, although it may appear in the model. Strong consistency is proved. In addition, in the case of truncated and tobit regression models, maximum score estimators allow restriction of the sample in order to make ordinary least squares method consistent.
Maximum score estimation is a class of semiparametric methods for the coefficients of regression models. Estimates are obtained by the maximization of the special function, called the score. In case of binary regression models it is the fraction of correctly classified observations. The aim of this article is to propose a modification to the score function. The modification allows to obtain smaller variances of estimators than the standard maximum score method without impacting other properties like consistency. The study consists of extensive Monte Carlo experiments.