# Deconvolution, convex optimization, non-parametric empirical Bayes and treatment of non-response

@article{Greenshtein2014DeconvolutionCO, title={Deconvolution, convex optimization, non-parametric empirical Bayes and treatment of non-response}, author={E. Greenshtein and Theodor Itskov}, journal={arXiv: Statistics Theory}, year={2014} }

Let $(Y_i,\theta_i)$, $i=1,...,n$, be independent random vectors distributed like $(Y,\theta) \sim G^*$, where the marginal distribution of $\theta$ is completely unknown, and the conditional distribution of $Y$ conditional on $\theta$ is known. It is desired to estimate the marginal distribution of $\theta$ under $G^*$, as well as functionals of the form $E_{G^*} h(Y,\theta)$ for a given $h$, based on the observed $Y_1,...,Y_n$.
In this paper we suggest a deconvolution method for the above…

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