Matrix analysis
Fundamentals of statistical signal processing: estimation theory
Fundamentals of statistical signal processing: estimation theory
CFAR detection of multidimensional signals: an invariant approach
IEEE Transactions on Signal Processing
The adaptive coherence estimator: a uniformly most-powerful-invariant adaptive detection statistic
IEEE Transactions on Signal Processing
Rao Test for Adaptive Detection in Gaussian Interference With Unknown Covariance Matrix
IEEE Transactions on Signal Processing - Part II
IEEE Transactions on Signal Processing
Adaptive array detection of uncertain rank one waveforms
IEEE Transactions on Signal Processing
Parametric GLRT for Multichannel Adaptive Signal Detection
IEEE Transactions on Signal Processing
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Three common techniques to discriminate between alternatives in a binary hypothesis testing problem are: the generalized likelihood ratio test (GLRT), the Rao test, and theWald test. In this paper, we investigate some characteristics of the corresponding decision statistics and provide their expressions for some problems of particular interest in statistical signal processing. First of all, we focus on the invariance of the Rao and Wald tests with respect to transformations leaving the testing problem unaltered. Then, we introduce necessary and sufficient conditions in order for their decision statistics to coincide with twice the logarithm of the GLRT statistic. Finally, we present some detection problems, usually encountered in practical signal processing applications, where the decision variables of the three quoted tests are equivalent, namely related by strictly monotonic transformations.