We study the statistical decision process of detecting the signal from a `signal+noise' type matrix model with an additive Wigner noise. We propose a hypothesis test based on the linear spectral statistics of the data matrix, which does not depend on the distribution of the signal or the noise. The test is optimal under the Gaussian noise if the signal-to-noise ratio is small, as it minimizes the sum of the Type-I and Type-II errors. Under the non-Gaussian noise, the test can be improved with an entrywise transformation to the data matrix. We also introduce an algorithm that estimates the rank of the signal when it is not known a priori.

翻译：我们研究从“信号+噪音”类型矩阵模型中检测信号的统计决策程序,该模型带有添加活性噪声;我们提议根据数据矩阵的线性光谱统计进行假设测试,不取决于信号的分布或噪音;如果信号对噪音比率小,则在高斯噪音下进行最优测试,因为信号对噪音比率小,因为它最大限度地减少了I型和II型错误的总和;在非Gausian噪音下,通过对数据矩阵进行切入式转换,可以改进测试;我们还引入一种算法,在不知道前置信息的情况下估计信号的等级。