Filtering Additive Measurement Noise with Maximum Entropy in the Mean

TL;DR

This paper demonstrates how the maximum entropy in the mean (MEM) method can enhance parameter estimation accuracy in noisy measurement scenarios, specifically for exponential distribution parameters, outperforming Bayesian and maximum likelihood methods.

Contribution

The paper introduces the application of MEM to improve parametric estimation under high noise levels, providing a comparative analysis with existing methods.

Findings

MEM outperforms Bayesian and MLE in noisy conditions

Enhanced robustness of parameter estimates with MEM

Applicable to exponential distribution parameter estimation

Abstract

The purpose of this note is to show how the method of maximum entropy in the mean (MEM) may be used to improve parametric estimation when the measurements are corrupted by large level of noise. The method is developed in the context on a concrete example: that of estimation of the parameter in an exponential distribution. We compare the performance of our method with the bayesian and maximum likelihood approaches.