论文标题
一般级别的尖刺Wigner模型中的弱检测
Weak Detection in the Spiked Wigner Model with General Rank
论文作者
论文摘要
我们研究了带有添加剂噪声的“信号+噪声”类型矩阵模型检测信号的统计决策过程。我们根据数据矩阵的线性光谱统计量提出了一个假设检验，该假设不取决于信号或噪声的分布。如果信噪比很小，则该测试在高斯噪声下是最佳的，因为它可以最大程度地减少I型和II型错误的总和。在非高斯噪声下，可以通过对数据矩阵的进入转换来改进测试。我们还引入了一种算法，该算法在不知道先验的信号时估计信号的等级。
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.
