Evaluation of a method's robustness

In signal processing, it is typical to develop or use a method based on a given model. In practice, however, we almost never know the actual model and we hope that the assumed model is in the neighborhood of the true one. If deviations exist, the method may be more or less sensitive to them. Therefore, it is important to know more about this sensitivity, or in other words, how robust the method is to model deviations. To that end, it is useful to have a metric that can quantify the robustness of the method. In this paper we propose a procedure for developing a variety of metrics for measuring robustness. They are based on a discrete random variable that is generated from observed data and data generated according to past data and the adopted model. This random variable is uniform if the model is correct. When the model deviates from the true one, the distribution of the random variable deviates from the uniform distribution. One can then employ measures for differences between distributions in order to quantify robustness. In this paper we describe the proposed methodology and demonstrate it with simulated data.