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MEASUREMENT ERROR AND DECONVOLUTION IN SPACES OF GENERALIZED FUNCTIONS

Published online by Cambridge University Press:  16 April 2014

Victoria Zinde-Walsh
Victoria Zinde-Walsh*
Affiliation:
McGill University and CIREQ
*
*Address correspondence to Victoria Zinde-Walsh, Department of Economics, McGill University, 855 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2T7; e-mail: victoria.zinde-walsh@mcgill.ca.
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Abstract

This paper considers convolution equations that arise from problems such as measurement error and nonparametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions to account for possible singularities; this makes it possible to consider densities for arbitrary and not only absolutely continuous distributions, and to operate with Fourier transforms for polynomially growing regression functions. Results are derived for identification and well-posedness in the topology of generalized functions for the deconvolution problem and for some regression models. Conditions for consistency of plug-in estimation for these models are provided.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 6 , December 2014 , pp. 1207 - 1246
Copyright
Copyright © Cambridge University Press 2014 

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