Nonparametric maximum likelihood methods for binary response models with random coefficients

Abstract

The venerable method of maximum likelihood has found numerous recent applications in nonparametric estimation of regression and shape constrained densities. For mixture models the NPMLE of Kiefer and Wolfowitz (1956) plays a central role in recent development of empirical Bayes methods. The NPMLE has also been proposed by Cosslett (1983) as an estimation method for single index linear models for binary response with random coefficients. However, computational difficulties have hindered its application. Combining recent developments in computational geometry and convex optimization we develop a new approach to computation for such models that dramatically increases their computational tractability. Consistency of the method is established for an expanded profile likelihood formulation. The methods are evaluated in simulation experiments, compared to the deconvolution methods of Gautier and Kitamura (2013) and illustrated in an application to modal choice for journey-to-work data in the Washington DC area.