论文标题
高维协方差矩阵的带子自适应测试
Adaptive Tests for Bandedness of High-dimensional Covariance Matrices
论文作者
论文摘要
高维带的协方差矩阵的估计广泛用于多元统计分析。为了确保估计的有效性，我们旨在测试以下假设：在高维框架下，协方差矩阵在一定的带宽中带宽。尽管文献中已经提出了几种测试方法，但现有测试仅适用于某些稀疏水平的某些替代方案，而对于具有其他稀疏结构的替代方案，它们可能并不强大。本文的目的是为高维协方差矩阵的束带提出新的测试，该测试对于具有各种稀疏水平的替代方案非常有力。提出的新测试还用于测试高维因子模型中误差向量的协方差矩阵的带状结构。基于这些统计数据，还为带宽的高维协方差矩阵引入了一致的带宽估计器。从蛋白质质谱法中进行了广泛的模拟研究和对前列腺癌数据集的应用，以评估带有带宽协方差矩阵的拟议自适应测试蓝色和带宽估计器的有效性。
Estimation of the high-dimensional banded covariance matrix is widely used in multivariate statistical analysis. To ensure the validity of estimation, we aim to test the hypothesis that the covariance matrix is banded with a certain bandwidth under the high-dimensional framework. Though several testing methods have been proposed in the literature, the existing tests are only powerful for some alternatives with certain sparsity levels, whereas they may not be powerful for alternatives with other sparsity structures. The goal of this paper is to propose a new test for the bandedness of high-dimensional covariance matrix, which is powerful for alternatives with various sparsity levels. The proposed new test also be used for testing the banded structure of covariance matrices of error vectors in high-dimensional factor models. Based on these statistics, a consistent bandwidth estimator is also introduced for a banded high dimensional covariance matrix. Extensive simulation studies and an application to a prostate cancer dataset from protein mass spectroscopy are conducted for evaluating the effectiveness of the proposed adaptive tests blue and bandwidth estimator for the banded covariance matrix.
