Measure Transformed Quasi Score Test with Application to Location Mismatch Detection

Abstract: In this paper, we develop a generalization of the Gaussian quasi score test (GQST) for composite binary hypothesis testing. The proposed test, called measure transformed GQST (MT-GQST), is based on the score-function of the measure transformed Gaussian quasi maximum likelihood estimator (MT-GQMLE) that operates by empirically fitting a Gaussian model to a transformed probability measure of the data. By judicious choice of the transform we show that, unlike the GQST, the proposed MT-GQST involves higher-order statistical moments and can gain resilience to outliers, leading to significant mitigation of the model mismatch effect on the decision performance. A data-driven procedure for optimal selection of the measure transformation parameters is developed that minimizes the spectral norm of the empirical asymptotic error-covariance of the MT-GQMLE. This amounts to maximization of an empirical worst-case asymptotic local power at a fixed asymptotic size. The MT-GQST is applied to location mismatch detection of a near-field point source in a simulation example that illustrates its robustness to outliers.