Running head: Deconvolution in generalized functions Victoria Zinde-Walsh Department of Economics, McGill University 855 Sherbrooke Street West, Montreal, Quebec, Canada H3A 2T7 

## Abstract 

This paper considers convolution equations that arise from problems such as measurement error and non-parametric regression with errors in variables with independence conditions. The equations are examined in spaces of gen- eralized functions to account for possible singularities; this makes it possible to consider densities for arbitrary and not only absolutely continuous dis- tributions, 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 derived. 

