We consider the problem of detecting (testing) Gaussian stochastic sequences (signals) with imprecisely known means and covariance matrices. The 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 explore 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.

翻译：本文研究均值与协方差矩阵不精确已知的高斯随机序列（信号）的检测（检验）问题。备择假设为独立同分布、均值为零、方差为1的高斯随机变量。在给定虚警概率（第一类错误概率）条件下，极小极大检测的质量由观测范围渐增时最优漏检概率（第二类错误概率）指数决定。本文探索了均值与协方差矩阵（复合假设）的最大集合，使得在不降低检测指数的前提下，其极小极大检验可被替换为对单一特定均值-协方差矩阵对（简单假设）的检验。我们完整刻画了这一最大集合。