We consider minimax signal detection in the sequence model. Working with certain ellipsoids in the space of square-summable sequences of real numbers, with a ball of positive radius removed, we obtain upper and lower bounds for the minimax separation radius in the non-asymptotic framework, i.e., for a fixed value of the involved noise level. We use very weak assumptions on the noise (i.e., fourth moments are assumed to be uniformly bounded). In particular, we do not use any kind of Gaussian distribution or independence assumption on the noise. It is shown that the established minimax separation rates are not faster than the ones obtained in the classical sequence model (i.e., independent standard Gaussian noise) but, surprisingly, are of the same order as the minimax estimation rates in the classical setting. Under an additional condition on the noise, the classical minimax separation rates are also retrieved in benchmark well-posed and ill-posed inverse problems.

中文翻译：

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弱噪声假设下的Minimax信号检测

我们在序列模型中考虑了minimax信号检测。在实数的平方和序列的空间中使用某些椭球，并移除正半径的球，我们获得了非渐近框架中minimax分离半径的上限和下限，即涉及的噪音水平。我们对噪声使用非常弱的假设（即，假设第四矩是均匀有界的）。特别是，我们不对噪声使用任何高斯分布或独立性假设。结果表明，所建立的极小极大分离率并不比经典序列模型中获得的极小极大分离率快（即独立的标准高斯噪声），​​但令人惊讶的是，它与经典环境中的极小极大估计率处于同一数量级。