A Unified Approach to Solve Ill - Posed Inverse Problems in Econometrics
نویسندگان
چکیده
We consider the general issue of estimating a nonparametric function φ from the inverse problem r = Tφ given estimates of the function r and of the linear transform T . Two typical examples include the estimation of a probability density function from data 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 φ as well as of its derivatives.
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