Minimum Contrast Empirical Likelihood Inference of Discontinuity in Density*
Minimum Contrast Empirical Likelihood Inference of Discontinuity in Density*
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DOI：
10.1080/07350015.2019.1617155
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发表时间：
2020-10
影响因子：
3
通讯作者：
Jun Ma;Hugo Jales;Zhengfei Yu
中科院分区：
文献类型：
--
作者：
Jun Ma;Hugo Jales;Zhengfei Yu
摘要本文研究了一种简单的基于经验似然的密度不连续推断方法的渐近性质。感兴趣的参数是概率密度函数在(可能)两个截止点的两个单边极限的函数。我们的方法是基于最小对比度问题的一阶条件。我们研究了该方法的一阶和二阶性质。我们对推理方法中的领先覆盖误差进行了刻画，并提出了覆盖误差最优的带宽选择器。我们证明了经验似然比统计量是Bartlett可校正的。一个重要的特例是回归不连续设计(RDD)中的操纵测试问题，其中感兴趣的参数是已知阈值下的密度差。在RDD中，分配变量密度在阈值处的连续性被认为是“无操纵”行为假设，这是局部平均处理效应的识别条件的可检验蕴涵。当专门用于操作测试问题时，CE-最优带宽选择器具有显式形式。我们提出了一种数据驱动的CE-最优带宽选择器，用于实际应用。给出了蒙特卡罗模拟的结果。通过一个实例说明了该方法的有效性。
Abstract This article investigates the asymptotic properties of a simple empirical-likelihood-based inference method for discontinuity in density. The parameter of interest is a function of two one-sided limits of the probability density function at (possibly) two cut-off points. Our approach is based on the first-order conditions from a minimum contrast problem. We investigate both first-order and second-order properties of the proposed method. We characterize the leading coverage error of our inference method and propose a coverage-error-optimal (CE-optimal, hereafter) bandwidth selector. We show that the empirical likelihood ratio statistic is Bartlett correctable. An important special case is the manipulation testing problem in a regression discontinuity design (RDD), where the parameter of interest is the density difference at a known threshold. In RDD, the continuity of the density of the assignment variable at the threshold is considered as a “no-manipulation” behavioral assumption, which is a testable implication of an identifying condition for the local average treatment effect. When specialized to the manipulation testing problem, the CE-optimal bandwidth selector has an explicit form. We propose a data-driven CE-optimal bandwidth selector for use in practice. Results from Monte Carlo simulations are presented. Usefulness of our method is illustrated by an empirical example.