In this section we shall discuss two important articles by Manski (1975) and Cosslett (1983). Both articles are concerned with the distribution-free estimation of parameters in QR models—Manski for multinomial models and Cosslett for binary models. However, their approaches are different: Manski proposed a nonparametric method called maximum score estimation whereas Cosslett proposed generalized maximum likelihood estimation in which the likelihood function is maximized with respect to both F and fi in the model
(9.2.1) . Both authors proved only consistency of their estimator but not asymptotic normality.