Nonparametric Maximum Likelihood Methods for Binary Response Models With Random Coefficients
结合计算几何与凸优化的最新进展，提出一种新的计算方法，使随机系数二元响应模型的非参数最大似然估计在计算上变得可行，并通过模拟和通勤方式选择数据验证了方法的有效性。
The venerable method of maximum likelihood has found numerous recent applications in nonparametric estimation of regression and shape constrained densities. For mixture models the nonparametric maximum likelihood estimator (NPMLE) of Kiefer and Wolfowitz plays a central role in recent developments of empirical Bayes methods. The NPMLE has also been proposed by Cosslett 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 and illustrated in an application to modal choice for journey-to-work data in the Washington DC area. Supplementary materials for this article are available online.