A Coverage Approach to Evaluating Mean Square Error

Bureau of Labor Statistics

Thursday, April 4, 2013 - 3:30pm

We propose a method for evaluating the mean square error (mse) of a possibly biased estimator $\hat\Theta_1$, or, rather, the class of estimators to which it belongs. The method uses confidence intervals c of a corresponding unbiased estimator $\hat\Theta$ and makes its assessment based on the extent to which c includes $\hat\Theta_1$. The method does not require an estimate, implicit or explicit, of the bias of $\hat\Theta_1$, is indifferent to the bias/variance breakdown of $\hat\Theta_1$’s mse, and does not require surety of the model on which $\hat\Theta_1$ is based.