Injectivity of a class of integral operators with compactly supported kernels
Injectivity of a class of integral operators with compactly supported kernels
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一类具有紧支持核的积分算子的内射性
DOI：
10.1016/j.jeconom.2017.05.013
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发表时间：
2017
影响因子：
6.3
通讯作者：
J. Shiu
中科院分区：
文献类型：
--
作者：
Yingyao Hu;Susanne M. Schennach;J. Shiu
积分算子的内射性与其对应的核函数的完备性条件有关。完备性提供了一个有用的方法，获得非参数识别在各种模型，包括非参数回归模型与工具变量，非经典测量误差模型，拍卖模型等，然而，条件是相当抽象的实证工作，缺乏适当的经济解释。我们依赖于已知的结果，关于沃尔泰拉方程提供充分条件的完备性条件的密度与紧的支持。我们的条件包括各种光滑性假设和单调移动的支持假设的核函数的运营商。我们应用我们的研究结果，建立非参数IV回归模型，非经典测量误差模型，拍卖模型的非参数识别与访问的解释，没有特定的功能形式的限制。
Injectivity of integral operators is related to completeness conditions of their corresponding kernel functions. Completeness provides a useful way of obtaining nonparametric identification in various models including nonparametric regression models with instrumental variables, nonclassical measurement error models, and auction models, etc. However, the condition is quite abstract for empirical work and lacks a proper economic interpretation. We rely on known results regarding the Volterra equation to provide sufficient conditions for completeness conditions for densities with compact support. Our conditions include various smoothness assumptions and monotonously moving support assumptions on the kernel function of the operator. We apply our results to establish nonparametric identification in nonparametric IV regression models, nonclassical measurement error models, and auction models with an accessible interpretation and without specific functional form restrictions.