Higher order detection test for deterministic signals

In the contex of electromagnetic signals, we want to detect a transient in a non stationnary gaussian noise by a higher order statistic test. In this paper, we use a new formalism (an extension of Gardner's work) that enables us to evaluate theoretically the response of higher order statistic test for detection. We develop the theoretical ground and we prove that higher order statistic detection test provides a very short delay detection. We apply our methods to simulation of a simple and typical example : the kurtosis.