Measuring Estimator's Credibility: Noncredibility Index

Many estimators and filters provide assessments (e.g., MSE matrices) of their own estimation errors. They are, however, obtained based on simplifying assumptions that are not necessarily valid. Then the questions are: Are these self-assessments trustable? How trustable are they? We referred to these problems as the credibility of the estimators/filters. Solid technical answers to the first question are provided in two companion papers for this conference based on statistical hypothesis testing. Complementary to those, we answer the second question in this paper by proposing a family of metrics, called noncredibility indices (NCI) and inclination indicators (I²), that measure how credible various self-assessments are. We show that the NCI and I have many desirable properties and are more appropriate than a bunch of possible alternatives and by far superior to a heuristic measure currently in use explicitly or implicitly. We also provide simple numerical examples to illustrate the application of the metrics proposed