A note on the properties of the confidence set for the local average treatment effect obtained by inverting the score test
反演得分检验得到的局部平均处理效应置信集性质AI 解读 ↓
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反演得分检验得到的局部平均处理效应置信集性质
- 研究问题
- 在允许任意弱工具变量的非参数和半参数模型中，局部平均处理效应的得分置信集有哪些形态，其与双重稳健 Wald 区间如何关联？
- 方法与思路
- 作者反演基于非参数影响函数估计的得分检验，刻画置信集形态，分析固定分布与局部弱工具渐近情形，并用模拟和计算算法展示结果。
- 材料陈述的贡献
- 摘要称，置信集有六种可能形态，在固定分布下与相应 Wald 区间渐近接近；弱工具下双重稳健点估计有偏且非正态，得分置信集模拟表现较好。
- 阅读关注点
- 应核对一致有效性与固定分布渐近结果的区别、空集或无界集出现的条件，以及直径最优性所需的影响函数关系和计算算法。
- 阅读边界
- 这是 arXiv 预印本，不能据此认定已同行评审或期刊接收；摘要未列出完整正则条件，直径最优性有附加前提，模拟表现不能推广至所有弱工具情形。
原文摘要
We study the properties of the score confidence set for the local average treatment effect in non and semiparametric instrumental variable models. This confidence set is constructed by inverting a score test based on an estimate of the nonparametric influence function for the estimand, and is known to be uniformly valid in models that allow for arbitrarily weak instruments; because of this, the confidence set can have infinite diameter at some laws. We characterize the six possible forms the score confidence set can take: a finite interval, an infinite interval (or a union of them), the whole real line, an empty set, or a single point. Moreover, we show that, at any fixed law, the score confidence set asymptotically coincides, up to a term of order 1/n, with the Wald confidence interval based on the doubly robust estimator which solves the estimating equation associated with the nonparametric influence function. This result implies that, in models where the efficient influence function coincides with the nonparametric influence function, the score confidence set is, in a sense, optimal in terms of its diameter. We also show that under weak instrument asymptotics, where the strength of the instrument is modelled as local to zero, the doubly robust estimator is asymptotically biased and does not follow a normal distribution. A simulation study confirms that, as expected, the doubly robust estimator performs poorly when instruments are weak, whereas the score confidence set retains good finite-sample properties in both strong and weak instrument settings. Finally, we provide an algorithm to compute the score confidence set, which is now available in the DoubleML package for double machine learning.