On the distribution of the conditional mean estimator in Gaussian noise

Document Type

Conference Proceeding

Publication Date

4-11-2021

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.

Identifier

85106177792 (Scopus)

ISBN

[9781728159621]

Publication Title

2020 IEEE Information Theory Workshop Itw 2020

External Full Text Location

https://doi.org/10.1109/ITW46852.2021.9457595

Grant

CCF-1908308

Fund Ref

National Science Foundation

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