Nonparametric Instrumental Variable Estimation Under Monotonicity
Nonparametric Instrumental Variable Estimation Under Monotonicity
复制标题
单调性下的非参数工具变量估计
DOI：
10.1920/wp.cem.2017.1417
复制
发表时间：
2015
期刊：
影响因子：
6.1
通讯作者：
D. Wilhelm
中科院分区：
文献类型：
--
作者：
D. Chetverikov;D. Wilhelm
非参数工具变量（NPIV）模型的不适定性导致估计量可能具有较差的统计性能。在本文中，我们探讨了施加形状限制，以提高性能的NPIV估计的可能性。我们假设要估计的函数是单调的，并考虑强制执行这种单调性约束的筛估计。我们定义了一个与约束估计相关的约束不适定性测度，并证明了在单调IV假设和某些其他温和的正则性条件下，该测度在筛空间的维数上一致有界。这一发现与众所周知的结果形成鲜明对比，即与无约束估计量相关的不适定性的无约束筛分测度随着筛分空间的维数增长到无穷大。基于这个结果，我们得到了一个新的非渐近误差界的约束估计。该界给出了一组数据生成过程，其中单调性约束具有特别强的正则化效果，并大大提高了估计量的性能。边界的形式意味着正则化效应即使在大样本中也可能很强，即使要估计的函数很陡，特别是如果NPIV模型严重不适定。我们的模拟研究证实了这些发现，并揭示了大的性能增益施加单调性约束的潜力。
The ill‐posedness of the nonparametric instrumental variable (NPIV) model leads to estimators that may suffer from poor statistical performance. In this paper, we explore the possibility of imposing shape restrictions to improve the performance of the NPIV estimators. We assume that the function to be estimated is monotone and consider a sieve estimator that enforces this monotonicity constraint. We define a constrained measure of ill‐posedness that is relevant for the constrained estimator and show that, under a monotone IV assumption and certain other mild regularity conditions, this measure is bounded uniformly over the dimension of the sieve space. This finding is in stark contrast to the well‐known result that the unconstrained sieve measure of ill‐posedness that is relevant for the unconstrained estimator grows to infinity with the dimension of the sieve space. Based on this result, we derive a novel non‐asymptotic error bound for the constrained estimator. The bound gives a set of data‐generating processes for which the monotonicity constraint has a particularly strong regularization effect and considerably improves the performance of the estimator. The form of the bound implies that the regularization effect can be strong even in large samples and even if the function to be estimated is steep, particularly so if the NPIV model is severely ill‐posed. Our simulation study confirms these findings and reveals the potential for large performance gains from imposing the monotonicity constraint.