Nonparametric and Distribution-Free Estimation of the Binary Choice and the Threshold-Crossing Models
This paper studies the problem of nonparametric identiﬁcation and estimation of binary threshold-crossing and binary choice models. First, conditions are given that guarantee the nonparametric identiﬁcation of both the function of exogenous observable variables and the distribution of the random terms. Second, the identiﬁcation results are employed to develop strongly consistent estimation methods that are nonparametric in both the function of observable exogenous variables and the distribution of the unobservable random variables. The estimators are obtained by maximizing a likelihood function over nonparametric sets of functions. A two-step constrained optimization procedure is devised to compute these estimators.
Matzkin, Rosa L., "Nonparametric and Distribution-Free Estimation of the Binary Choice and the Threshold-Crossing Models" (1988). Cowles Foundation Discussion Papers. 1133.