A Coverage Approach to Evaluating Mean Square Error

We propose a new method for evaluating the mean square error (mse) of a possibly biased estimator 1̂ θ , or, rather, the class of estimators to which it belongs. The method uses confidence intervals c of a corresponding unbiased estimator θ̂ and makes its assessment based on the extent to which c includes 1̂ θ . The method does not require an estimate, implicit or explicit, of the bias of 1̂ θ , is indifferent to the bias/variance breakdown of 1̂ θ ’s mse, and does not require surety of a model on which 1̂ θ is based.