Minimum Error Entropy Estimation Under Contaminated Gaussian Noise

is shown that R & eacute;nyi's entropy of a Gaussian mixture with entropic index alpha is an element of (1, infinity] is upper-bounded by the cluster with minimum variance. This basic idea leads to a clean worst-case formulation of the minimum error entropy principle in the context of linear multi-sensor fusion by using a largely contaminated Gaussian distribution to model sensor errors with outliers. The obtained entropic best linear unbiased estimator leads to an operational interpretation in terms of a precision/reliability trade-off, it resonates closely with model-order selection methods, and it provides a possible information-theoretic root to sparsity promoting regularization.