标题： 非参数模型中基于独立性条件的识别与适定性问题 显示英文标题

标题： Identification and well-posedness in nonparametric models with independence conditions

摘要： 本文对几类模型进行了非参数分析，其中包括经典测量误差、变量误差回归、因子模型以及其他可以用卷积方程形式表示的模型。 这里关注的是解的存在性条件、非参数识别以及广义函数空间（缓增广义函数）中的适定性问题。 与在函数空间中工作相比，这一空间通过放宽假设并扩展结果，能够涵盖更广泛的模型种类，例如无需密度存在性假设。 定义了解存在的（广义）函数类，并讨论了识别条件、部分识别及其含义。 给出了适定性的条件，并考察了与之相关的插件估计和正则化问题。 显示英文摘要

摘要： This paper provides a nonparametric analysis for several classes of models, with cases such as classical measurement error, regression with errors in variables, factor models and other models that may be represented in a form involving convolution equations. The focus here is on conditions for existence of solutions, nonparametric identification and well-posedness in the space of generalized functions (tempered distributions). This space provides advantages over working in function spaces by relaxing assumptions and extending the results to include a wider variety of models, for example by not requiring existence of density. Classes of (generalized) functions for which solutions exist are defined; identification conditions, partial identification and its implications are discussed. Conditions for well-posedness are given and the related issues of plug-in estimation and regularization are examined.