New Concentration Metrics for Performance Evaluation of Estimation Algorithms

Different estimators have different optimization criteria according to the concrete application considered. Most existing metrics on estimation performance are some averages of estimation errors, which usually give "big" or "small" results to show the "bad" or "good" performance of the evaluated estimators. However, these metrics are only appropriate for measuring minimum mean-square error (MMSE), linear MMSE and even least square estimators and have bias on ones like maximum a posteriori estimators. To handle this problem, a concentration measure is proposed in [1] to measure how concentrative the estimation errors are relative to a desired probability density function. This study proposed several concentration measures including both relative and absolute ones. And the existing concentration measure is extended to more general cases. Illustration examples are provided to verify the effectiveness of our proposed measures.