Robust composite binary hypothesis testing via measure-transformed quasi score test

Abstract

• This paper handles the problem of composite binary hypothesis testing when an accurate probability model is not available. • Under this framework, a robust generalization of the Gaussian quasi score test is developed. • The proposed generalization, assumes a Gaussian model after applying a transform to the probability measure of the data. • The considered measure-transformation is structured by a non-negative data weighting function, called MT-function. • Proper selection of the MT-function leads to significant mitigation of the model mismatch effect. This paper deals with the problem of composite binary hypothesis testing when an accurate parametric probability model is not available. Under this framework, a robust generalization of the Gaussian quasi score test (GQST) is developed. The proposed generalization, called measure-transformed (MT) GQST assumes a Gaussian probability model after applying a transform to the probability measure (distribution) of the data. The considered measure-transformation is structured by a non-negative data weighting function, called MT-function. By proper selection of the MT-function, we show that, unlike the GQST, the proposed MT-GQST can gain resilience against heavy-tailed noise outliers, leading to significant mitigation of the model mismatch effect (introduced by the normality assumption), and yet, have the implementation advantages of the standard GQST (arising from the convenient Gaussian model). The proposed MT-GQST is applied for testing the vector parameters of linear and nonlinear multivariate data models. Simulation examples illustrate its advantages as compared to the GQST and other robust detectors.