Estimation of A Class of Nonparameteric Probit Models

Abstract

In this paper, we consider a class of nonparametric probit models for binary dependent variables. We extend the standard parametric probit models to nonparametric models in which the parametric index function in the standard probit models is nonparametrically specified. Such a nonparametric specification for the index function in probit models allows us to consider a flexible functional form of the structural parameters. We propose to use a sieve maximum likelihood estimation approach to estimate the parameter and develop the asymptotic theory, including consistency, convergence rates, and asymptotic normality. Our asymptotic normality results are applicable to a wide class of functionals of the parameter, regardless of whether the functional of interest is regular or irregular. The Monte Carlo simulation result shows that the proposed sieve maximum likelihood estimator performs well in finite samples in the sense that the proposed sieve maximum likelihood estimator has a small variance and negligible bias in finite samples.