Comments on "An axiomatic construction of quadratic NAR power estimators for adaptive detection" [with reply]

An unstated axiom in the abovementioned correspondence by M.H. El-Ayadi (see ibid., vol.ASSP-35, p.1347-50, Sept.1987) on quadratic noise estimators requires the kernel matrix to be nonnegative definite. The commenter shows that this assumption is not required for the noise-alone-reference (NAR) estimator; it limits the performance of the generalized NAR estimator in the sense of a minimum-variance unbiased statistic, and it provides the basis of a compromise between variance and bias used to derive the quasi-NAR estimator. It is observed that the nonnegative definite assumption is only one way of introducing a priori information as to the strictly positive nature of power. While this is a reasonable approach, it is not the only one, and it may be possible to realize improved performance in some cases by utilizing other means to introduce the a priori information together with application-specific optimization criteria. The author disagrees with the commenter and presents an argument substantiating his position. He points out that the nonnegative definite constraint is the only approach that makes the class of quadratic estimators considered take on nonnegative values for all possible observation vectors and that removing it does not necessarily result in smaller variance. He contends that the commenter deemphasizes the effect of estimator bias on detection performance.<>