Tldr; I am wondering If there is a test that enables you to compare two samples A and B of data, and robustly test the hypothesis that A contains a real signal, if B is certain to contain no signal, and they otherwise draw from identical sources of noise.

Some more details: I am working on a research project similar in setup to LIGO to look for a new physical phenomenon that would manifest as a signal sweeping through multiple detectors scattered around the world simultaneously. Because of the directional sensitivities of the detectors, there is a subset of possible data that cannot be associated with a real direction of propagation, and so can be identified as spurious.

My idea was that for N detectors, the data for each point in time can be considered a single vector in an N-dimensional space which just has the measured signal strength in each detector as the components. Then, true signals must reside in a 3D subspace which is spanned by a signal propagating in the x, y, and z directions. On the other hand, there is a unlimited choice of 3D subspaces orthogonal to the "real signal" subspace, and this should look identical to the real signal subspace if the data is explained purely by noise. However, if there is a very large signal in the real signal subspace compared to the data in the orthogonal one, I would like to be able to quantify the significance of that observation without having to resort to assumptions that the strength of the noise follows a particular statistical distribution. I'm stuck on this - any tips or resources where I can learn more about this type of statistics?

Thank you!!!


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