论文标题
在不平等约束下经常收缩
Frequentist Shrinkage under Inequality Constraints
论文作者
论文摘要
本文展示了如何缩小受经济理论促进的不平等限制的极值估计。我们提出了一个不等式约束的收缩估计器（ICSE），该估计量（ICSE）以与数据相关的权重以不平等和不等式约束的估计量之间的加权平均形式。重量驱动着收缩的方向和程度。我们使用局部渐近框架来得出ICSE的渐近分布和风险。我们提供的条件严格低于不受限制的极值估计器的渐近风险。在局部渐近框架下不能一致估计收缩程度。为了解决此问题，我们提出了可行的插件估计器并研究其有限的样本行为。我们还将我们的框架应用于Slutsky限制下的汽油需求估计。
This paper shows how to shrink extremum estimators towards inequality constraints motivated by economic theory. We propose an Inequality Constrained Shrinkage Estimator (ICSE) which takes the form of a weighted average between the unconstrained and inequality constrained estimators with the data dependent weight. The weight drives both the direction and degree of shrinkage. We use a local asymptotic framework to derive the asymptotic distribution and risk of the ICSE. We provide conditions under which the asymptotic risk of the ICSE is strictly less than that of the unrestricted extremum estimator. The degree of shrinkage cannot be consistently estimated under the local asymptotic framework. To address this issue, we propose a feasible plug-in estimator and investigate its finite sample behavior. We also apply our framework to gasoline demand estimation under the Slutsky restriction.
