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摘要翻译：
本文讨论了半参数M-估计的渐近理论，该估计一般适用于在一个或几个参数指标中满足单调性条件的模型。由于我们的估计量在应用于Manski(1975，1985)的二元选择模型时涉及一个第一阶段的非参数回归，所以我们称之为两阶段最大得分估计量(TSMS)。我们刻画了TSMS估计量的渐近分布，它的相变依赖于维数，从而依赖于第一阶段估计的收敛速度。我们证明了当第一步估计的维数较低时，TSMS估计与平滑最大得分估计(Horowitz，1992)是渐近等价的，而当维数不太高时，TSMS估计仍然实现相对于三次根速率的部分速率加速。第一阶段非参数估计器实际上是一个非光滑准则函数上的不完全光滑函数，导致第一阶段估计误差相对于第二阶段收敛速度和渐近分布的枢轴性
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英文标题：
《Two-Stage Maximum Score Estimator》
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作者：
Wayne Yuan Gao, Sheng Xu
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最新提交年份：
2020
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分类信息：
一级分类：Economics 经济学
二级分类：Econometrics 计量经济学
分类描述：Econometric Theory, Micro-Econometrics, Macro-Econometrics, Empirical Content of Economic Relations discovered via New Methods, Methodological Aspects of the Application of Statistical Inference to Economic Data.
计量经济学理论，微观计量经济学，宏观计量经济学，通过新方法发现的经济关系的实证内容，统计推论应用于经济数据的方法论方面。
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英文摘要：
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. We show that the TSMS estimator is asymptotically equivalent to the smoothed maximum-score estimator (Horowitz, 1992) when the dimension of the first-step estimation is relatively low, while still achieving partial rate acceleration relative to the cubic-root rate when the dimension is not too high. 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
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PDF链接：
https://arxiv.org/pdf/2009.02854
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