Sensitivity of some optimal detectors to noise skewness

This paper evaluates and compares the sensitivity of the sample mean detector and the sign detector to the underlying noise skewness. The performances of the detectors are evaluated via the false-alarm rate, the power, and the probability of error. A Cornish-Fisher type asymptotic expansion is utilized so that asymptotic relations between the skewness measure and the detector performance are obtained. The noise model used here is nearly Gaussian, being perturbed by a small amount of skewness. When the skewness measure is greater than zero, the associated density function exhibits a heavier tail at the right side of the origin but still possesses zero mean (but not zero median, of course). For this particular model, it is found that the sign detector is less sensitive than the sample mean detector to this skewness. Some curves are given which provide a clearer insight into the rate of change of the performance of both detectors.