We propose a new estimator for nonparametric binary choice models that does not impose a parametric structure on either the systematic function of covariates or the distribution of the error term. A key advantage of our approach is its computational efficiency. For instance, even when assuming a normal error distribution as in probit models, commonly used sieves for approximating an unknown function of covariates can lead to a large-dimensional optimization problem when the number of covariates is moderate. Our approach, motivated by kernel methods in machine learning, views certain reproducing kernel Hilbert spaces as special sieve spaces, coupled with spectral cut-off regularization for dimension reduction. We establish the consistency of the proposed estimator for both the systematic function of covariates and the distribution function of the error term, and asymptotic normality of the plug-in estimator for weighted average partial derivatives. Simulation studies show that, compared to parametric estimation methods, the proposed method effectively improves finite sample performance in cases of misspecification, and has a rather mild efficiency loss if the model is correctly specified. Using administrative data on the grant decisions of US asylum applications to immigration courts, along with nine case-day variables on weather and pollution, we re-examine the effect of outdoor temperature on court judges' "mood", and thus, their grant decisions.

翻译：我们提出了一种新的非参数二元选择模型估计器，该估计器不对协变量的系统函数或误差项的分布施加参数化结构。我们方法的一个关键优势在于其计算效率。例如，即使在假设误差服从正态分布（如probit模型）的情况下，当协变量数量适中时，常用的用于近似未知协变量函数的筛空间可能导致高维优化问题。受机器学习中核方法的启发，我们的方法将某些再生核希尔伯特空间视为特殊的筛空间，并结合谱截断正则化进行降维。我们证明了所提估计器对于协变量的系统函数和误差项的分布函数的一致性，以及加权平均偏导数的插件估计量的渐近正态性。模拟研究表明，与参数估计方法相比，所提方法在模型设定错误的情况下能有效改善有限样本性能，而在模型正确设定时效率损失相当温和。利用美国移民法庭庇护申请裁决的行政数据，以及关于天气和污染的九个案件-日期变量，我们重新审视了室外温度对法庭法官"情绪"及其裁决结果的影响。