@inproceedings{dadc6082ca214ae8aba0ea924b45c7f4,

title = "On the distribution of the conditional mean estimator in Gaussian noise",

abstract = "Consider the conditional mean estimator of the random variable X from the noisy observation Y = X + N where N is zero mean Gaussian with variance σ2 (i.e., E[X|Y ]). This work characterizes the probability distribution of E[X|Y ]. As part of the proof, several new identities and results are shown. For example, it is shown that the k-th derivative of the conditional expectation is proportional to the (k + 1)-th conditional cumulant. It is also shown that the compositional inverse of the conditional expectation is well-defined and is characterized in terms of a power series by using Lagrange inversion theorem.",

keywords = "Conditional mean estimator, Gaussian Noise",

author = "Alex Dytso and {Vincent Poor}, H. and Shlomo Shamai",

note = "Funding Information: This work was supported in part by the U. S. National Science Foundation under Grant CCF-1908308 and by the United States-Israel Binational Science Foundation, under Grant BSF-2018710. Publisher Copyright: {\textcopyright}2021 IEEE; 2020 IEEE Information Theory Workshop, ITW 2020 ; Conference date: 11-04-2021 Through 15-04-2021",

year = "2021",

month = apr,

day = "11",

doi = "10.1109/ITW46852.2021.9457595",

language = "English (US)",

series = "2020 IEEE Information Theory Workshop, ITW 2020",

publisher = "Institute of Electrical and Electronics Engineers Inc.",

booktitle = "2020 IEEE Information Theory Workshop, ITW 2020",

address = "United States",

}