Identification and well-posedness in nonparametric models with independence conditions

Abstract

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.