@inproceedings{5ec30eee2c844a54b16b34d223a4d30f,
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 = "Publisher Copyright: {\textcopyright}2021 IEEE; 2020 IEEE Information Theory Workshop, ITW 2020 ; Conference date: 11-04-2021 Through 15-04-2021",
year = "2020",
doi = "10.1109/ITW46852.2021.9457595",
language = "الإنجليزيّة",
series = "2020 IEEE Information Theory Workshop, ITW 2020",
booktitle = "2020 IEEE Information Theory Workshop, ITW 2020",
}