Composite Hypothesis Tests for Detection of Modeling Misspecification

The performance of model-based signal processing inference methods may significantly degrade due to model errors. Thus, detection of model misspecification (MM) is essential in many applications. One of the most prominent MM detection approaches is based on comparison between the empirical characteristic function (CF) and the CF of the assumed model. However, there is no concrete or optimal method to extract the relevant information for MM detection. Another popular approach for MM detection is the information matrix test (IMT), which is based on the Cramér-Rao bound (CRB) regularity condition. This method is insensitive in some basic problems and it requires a twice continuously-differentiable probability density function of the observation under the null hypothesis. In order to address these issues, three new methods for MM detection are proposed in this paper. In the first method, it is proposed to address the CF frequency selection question via an optimization procedure, yielding the optimized characteristic function test (OCFT). In addition, a local version of the OCFT, called the optimized local characteristic function test (OLCFT), which combines information obtained from the CF and information matrix equality, is proposed. This test stems from the generalization of both the CF and the CRB regularity condition. In order to address the differentiabilty limitation, the IMT for MM detection is extended by a finite-difference form, named, discrete IMT (DIMT). Thus, it is applicable for discrete-valued parameters or classification problems. The performances of the proposed methods are studied via several signal processing examples.