SIMPLE SEMIPARAMETRIC ESTIMATION OF ORDERED RESPONSE MODELS
针对误差分布未知的有序响应模型，提出了两种无需调参的半参数估计方法，自动融入分布函数的单调性约束，得到回归系数和阈值参数的一致渐近正态估计，并开发了有效的bootstrap推断程序。
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.