Abstract:
We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. An alternative is independent
identically distributed zero-mean Gaussian random variables with unit variances. For a given
false alarm (1st-kind error) probability, the quality of minimax detection is given by the best
miss probability (2nd-kind error probability) exponent over a growing observation horizon. We
study the maximal set of means and covariance matrices (composite hypothesis) such that its
minimax testing can be replaced with testing a single particular pair consisting of a mean
and a covariance matrix (simple hypothesis) without degrading the detection exponent. We
completely describe this maximal set.
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