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Estimation Under Communication Constraints

  • Rudolf AhlswedeEmail author
Chapter
Part of the Foundations in Signal Processing, Communications and Networking book series (SIGNAL, volume 15)

Abstract

We analyze the following model: One person, called “helper” observes an outcome\(x^n=(x_1,\dots ,x_n)\in {\mathcal X}^n\) of the sequence \(X^n=(X_1,\dots ,X_n)\) of i.i.d. RV’s and the statistician gets a sample\(y^n=(y_1,\dots ,y_n)\) of the sequence \(Y^n(\theta ,x^n)\) of RV’s with a density \(\prod _{t=1}^n f(y_t|\theta , x_t)\). The helper can give some (side) information about \(x^n\) to the statistician via an encoding function \(s^n:{\mathcal X}^n\rightarrow \mathbb {N}\) with \(\text {rate} (s_n)\triangleq (1/n)\log \# \text {range}(s_n)\le R\). Based on the knowledge of \(s_n(x^n)\) and \(y^n\) the statistician tries to estimate \(\theta \) by an estimator \(\hat{\theta }_n\).

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.BielefeldGermany

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