Allerton 2015 Paper Abstract

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Paper ThC5.3

Chung, Hye Won (University of Michigan), Sadler, Brian (Army Research Laboratory), Hero, Alfred (University of Michigan)

Bounds on Variance for Symmetric Unimodal Distributions

Scheduled for presentation during the Regular Session "Detection and Estimation" (ThC5), Thursday, October 1, 2015, 14:10−14:30, Lower Level

53rd Annual Allerton Conference on Communication, Control, and Computing, Sept 29-Oct 2, 2015, Allerton Park and Retreat Center, Monticello, IL, USA

This information is tentative and subject to change. Compiled on November 19, 2019

Keywords Detection and Estimation, Information Theory

Abstract

We show a direct relationship between the variance and the differential entropy for the general class of symmetric unimodal distributions by providing an upper bound on variance in terms of entropy power. Combining this bound with the well-known entropy power lower bound on variance, we prove that for the general class of symmetric unimodal distributions the variance can be bounded below and above by the scaled entropy power. As differential entropy decreases, the variance is sandwiched between two exponentially decreasing functions in the differential entropy. This establishes that for the general class of symmetric unimodal distributions, the differential entropy can be used as a surrogate for concentration of the distribution.

 

 

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