We propose two simple semiparametric estimation methods for ordered response models with an unknown error distribution. The proposed methods do not require users to choose any tuning parameters, and they automatically incorporate the monotonicity restriction of the unknown distribution function. Fixing finite-dimensional parameters in the model, we construct nonparametric maximum likelihood estimates for the error distribution based on the related binary choice data or the entire ordered response data. We then obtain estimates for finite-dimensional parameters based on moment conditions given the estimated distribution function. Our semiparametric approaches deliver root-n consistent and asymptotically normal estimators of the regression coefficient and threshold parameter. We also develop valid bootstrap procedures for inference. The advantages of our methods are borne out in simulation studies and a real data application.

我们提出了两种简单的半参数估计方法，用于具有未知误差分布的有序响应模型。所提出的方法不需要用户选择任何调整参数，并且它们自动合并未知分布函数的单调性限制。固定模型中的有限维参数，我们基于相关的二元选择数据或整个有序响应数据构建误差分布的非参数最大似然估计。然后，我们根据给定估计分布函数的矩条件获得有限维参数的估计。我们的半参数方法提供了回归系数和阈值参数的n根一致且渐近正态的估计量。我们还开发了有效的推理引导程序。我们的方法的优点在模拟研究和实际数据应用中得到了证实。