Singular Gaussian Measures in DeGction Theory*

In the “statistical theory of signal detection,’’ as I understand the phrase, we are concerned with problems occurring in electrical communication engineering involving statistical inference from stochastic processes. Most of the work in this area has been directed to the theory of detecting or characterizing information-bearing signals immersed in noise with Gaussian statistics. It is one aspect of this narrower class of problems, the singular cases and what they imply about the suitability of the formulation, that is discussed here. We start from the model y ( t ) = s ( t ) + n(t) , (1)