论文标题
两阶段最高分数估计器
Two-Stage Maximum Score Estimator
论文作者
论文摘要
本文考虑了半参数M-估计器的渐近理论，该理论通常适用于满足一个或几个参数指数中单调性条件的模型。我们称估计器两阶段最高得分（TSM）估计量，因为我们的估计器涉及到Manski的二进制选择模型（1975，1985）时，涉及第一阶段的非参数回归。我们表征了TSMS估计量的渐近分布，该分布的特征是相变的，具体取决于尺寸，从而取决于第一阶段估计的收敛速率。有效地，第一阶段的非参数估计器在非平滑标准函数上充当不完美的平滑函数，导致第一阶段估计误差相对于第二阶段的收敛速率和渐近分布的关键性
This paper considers the asymptotic theory of a semiparametric M-estimator that is generally applicable to models that satisfy a monotonicity condition in one or several parametric indexes. We call the estimator two-stage maximum score (TSMS) estimator since our estimator involves a first-stage nonparametric regression when applied to the binary choice model of Manski (1975, 1985). We characterize the asymptotic distribution of the TSMS estimator, which features phase transitions depending on the dimension and thus the convergence rate of the first-stage estimation. Effectively, the first-stage nonparametric estimator serves as an imperfect smoothing function on a non-smooth criterion function, leading to the pivotality of the first-stage estimation error with respect to the second-stage convergence rate and asymptotic distribution
