On the MSE robustness of batching estimators

Variance is a classical measure of a point estimator´s sampling error. In steady-state simulation experiments, many estimators of this variance-or its square root, the standard error-depend upon batching the output data. In practice, the optimal batch size is unknown because it depends upon unknown statistical properties of the simulation output data. When optimal batch size is estimated, the batch size used is random. Therefore, robustness to estimated batch size is a desirable property for a standard-error estimation method. We consider only point estimators that are a sample mean of steady-state data and consider only mean squared error (MSE) as the criterion for comparing standard-error estimation methods. Like previous authors, we measure robustness as a second derivative. We argue that a previous measure the second derivative of MSE with respect to estimated batch size-is conceptually flawed. We propose a new measure, the second derivative of the MSE with respect to the estimated center of gravity of the non-negative autocorrelations of the output process. With the previous robustness measure, optimal MSE and robustness yielded different rankings of estimation methods. A property of the new robustness measure is that both criteria yield identical rankings