Detection of Modeling Misspecification Using Cross-Entropy Test

In many signal processing applications and learning problems, modeling misspecification may dramatically degrade the estimation performance. Thus, it is useful to detect possible misspecification in the model using the observations. In this work, a composite hypothesis test for detection of modeling misspecification is proposed in the non-Bayesian framework. The test is based on the estimated cross-entropy and thus it is called cross-entropy test (CET). It is computed by the negative of the maximized log-likelihood with respect to the unknown deterministic parameters, where the unknown deterministic parameters are substituted with their maximum likelihood estimates. It is shown that under some mild conditions, the proposed test has the constant false-alarm rate property. The CET performance is evaluated and compared via simulations to White's test for modeling misspecification detection, which is based on information matrix equality. In an example of direction-of-arrival estimation using a miscalibrated array of sensors, it is shown that unlike White's test, the CET is able to detect model misspecification.