Measure Transformed Quasi Score Test with Application to Location Mismatch Detection

TL;DR

This paper introduces the measure transformed GQST, a robust hypothesis test that leverages higher-order moments and measure transformations to improve detection performance under model mismatch and outliers.

Contribution

It generalizes the Gaussian quasi score test by incorporating measure transformations, enhancing robustness and resilience to outliers in hypothesis testing.

Findings

The proposed MT-GQST improves detection robustness against outliers.

Optimal measure transformation parameters enhance test performance.

Application to location mismatch detection demonstrates effectiveness.

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.