Robust alternative to statistical efficiency

Statistical efficiency is a common measure of the quality of an estimator. Typically, it’s expressed via the mean square error (\(\operatorname{MSE}\)). For the given estimator \(T\) and the true parameter value \(\theta\), the \(\operatorname{MSE}\) can be expressed as follows: \[\operatorname{MSE}(T) = \operatorname{E}[(T-\theta)^2] \] In numerical simulations, the \(\operatorname{MSE}\) can’t be used as a robust metric because its breakdown point is zero (a corruption of a single measurement ...

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