Measurement error and deconvolution in spaces of generalized functions
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 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 derived.
Cite
@article{arxiv.1009.4217,
title = {Measurement error and deconvolution in spaces of generalized functions},
author = {Victoria Zinde-Walsh},
journal= {arXiv preprint arXiv:1009.4217},
year = {2012}
}
Comments
This is a revised version of the paper "Measurement Error and Deconvolution in Generalized Functions Spaces". The revision maintains the focus on the two types of equations, the convolution equation and the system of equations; this version does not include Theorems 6 and 7