An Invariance Property of the Generalized Likelihood Ratio Test
Date of Original Version
The generalized likelihood ratio test (GLRT) is invariant with respect to transformations for which the hypothesis testing problem itself is invariant. This result from the statistics literature is presented in the context of some simple signal models. This is an important property of the GLRT in light of its widespread use and the recent interest in invariant tests applied to signal processing applications. The GLRT is derived for some examples in which the uniformly most powerful invariant (UMPI) test does and does not exist, including one in which the UMPI test exists and is not given by the GLRT.
IEEE Signal Processing Letters
Kay, Steven M., and Joseph R. Gabriel. "An Invariance Property of the Generalized Likelihood Ratio Test." IEEE Signal Processing Letters 10, 12 (2003): 352-355. doi:10.1109/LSP.2003.818865.