Measure-transformed Gaussian quasi score test

In this paper, we develop a robust 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 a transformation applied to the probability distribution of the data. The considered transform is structured by a non-negative function, called MT-function, that weights the data points. By appropriate selection of the MT-function we show that, unlike the GQST, the proposed MT-GQST incorporates higher-order moments and can gain robustness to outliers. The MT-GQST is applied for testing the parameter of a non-linear model. Simulation example illustrates its advantages as compared to the standard GQST and other robust detectors.