Mean square error performance of sample mean and sample median estimators

Based on the Ziv-Zakai methodology to bound estimators, we derived an estimation bound able to predict the mean square error degradation due to model mismatches. In this article, we build upon this result to provide a performance comparison between mean and median estimators in the presence of outliers. The latter is well known to be statistically more robust than the mean in the presence of outliers. Here we show this superiority by comparing their theoretical error bounds. Analytical results are obtained, which are validated by computer simulations.