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date: 12 November 2019

Abstract and Keywords

This chapter provides a nonparametric analysis for several classes of models, with cases such as classical measurement error, regression with errors in variables, 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 S* 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.

Keywords: nonparametric identification, deconvolution, generalized functions

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