Binary Hypothesis Testing via Measure Transformed Quasi-Likelihood Ratio Test

In this paper, the Gaussian quasi-likelihood ratio test (GQLRT) for non-Bayesian binary hypothesis testing is generalized by applying a transform to the probability distribution of the data. The proposed generalization, called measure-transformed GQLRT (MT-GQLRT), selects a Gaussian probability model that best empirically fits a transformed probability measure of the data. By judicious choice of the transform, we show that, unlike the GQLRT, the proposed test is resilient to outliers and involves higher order statistical moments leading to significant mitigation of the model mismatch effect on the decision performance. A Bayesian extension of the proposed MT-GQLRT is also developed that is based on selection of a Gaussian probability model that best empirically fits a transformed conditional probability distribution of the data. The non-Bayesian and Bayesian MT-GQLRTs are applied to signal detection and classification, in simulation examples that illustrate their advantages over the standard GQLRT and other robust alternatives.