Filtering Additive Measurement Noise with Maximum Entropy in the Mean

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.