论文标题
与非负部分相关性的协方差估计
Covariance estimation with nonnegative partial correlations
论文作者
论文摘要
我们研究了局部相关性无负相关的约束，研究高维协方差估计的问题。符号约束极大地简化了估计：高斯最大似然估计器的定义很好，只有两个观测值，而不管变量的数量如何。我们在尺寸可能比样本量大得多的环境中分析其性能。我们确定估计量在对称的Stein损失中既具有高维度一致性，又是最小值。我们还证明了一个负结果，该结果表明，标志可能会引入实质性偏见，以估计协方差矩阵的最高特征值。
We study the problem of high-dimensional covariance estimation under the constraint that the partial correlations are nonnegative. The sign constraints dramatically simplify estimation: the Gaussian maximum likelihood estimator is well defined with only two observations regardless of the number of variables. We analyze its performance in the setting where the dimension may be much larger than the sample size. We establish that the estimator is both high-dimensionally consistent and minimax optimal in the symmetrized Stein loss. We also prove a negative result which shows that the sign-constraints can introduce substantial bias for estimating the top eigenvalue of the covariance matrix.
