Nonparametric maximum likelihood methods for binary response models with random coefficients by Roger Koenker

Single index linear models for binary response with random coefficients have been
extensively employed in many econometric settings under various parametric specifications of
the distribution of the random coefficients. Nonparametric maximum likelihood estimation
(NPMLE) as proposed by Cosslett (1983) and Ichimura and Thompson (1998) in contrast, has
received less attention in applied work due primarily to computational difficulties.
We propose a new approach to computation of NPMLEs for binary response
models that significantly increase their computational tractability
thereby facilitating greater flexibility in applications. Our approach, which relies on
recent developments involving the geometry of hyperplane arrangements, is contrasted
with the recently proposed deconvolution method of Gautier and Kitamura (2013). An application to
modal choice for the journey to work in the Washington DC area illustrates the methods.