A unified approach to solve ill-posed inverse problems in econometrics

Jan Johannes, Sébastien van Belleghem and Anne Vanhems ()
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Sébastien van Belleghem: Université catholique de Louvain (UCL). Center for Operations Research and Econometrics (CORE)
Authors registered in the RePEc Author Service: Sebastien Van Bellegem ()

No 2007083, LIDAM Discussion Papers CORE from Université catholique de Louvain, Center for Operations Research and Econometrics (CORE)

Abstract: We consider the general issue of estimating a nonparametric function x from the inverse problem r = Tx given estimates of the function r and of the linear transform T. Two typical examples include the estimation of a probability density function fromdata contaminated by a noise whose distribution is unknown (blind deconvolution) and the nonparametric instrumental regression. We provide a unified framework based on Hilbert scales that synthesizes most of existing results in the econometric literature and also covers new relevant structural models. Results are given on the rate of convergence of the estimator of x as well as of its derivatives.

Keywords: inverse problem; Hilbert scale; deconvolution; instrumental variable; nonparametric regression (search for similar items in EconPapers)
JEL-codes: C14 C30 (search for similar items in EconPapers)
Date: 2007-10-01
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:cor:louvco:2007083

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