期刊名称：CORE Discussion Papers / Center for Operations Research and Econometrics (UCL), Louvain
出版年度：2007
卷号：1
出版社：Center for Operations Research and Econometrics (UCL), Louvain
摘要：We consider the general issue of estimating a nonparametric function . from the inverse
problem r = T. 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 . as well as of its derivatives.
