论文标题
对高维矢量自动进展的统计推断，测量误差
Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error
论文作者
论文摘要
在各种科学和业务应用中，经常遇到具有测量误差的高维矢量自动进度。在本文中，我们研究了该模型下过渡矩阵的统计推断。尽管有大量文献研究过渡矩阵的稀疏估计，但推理溶液的差异很少，尤其是在高维情况下。我们为过渡矩阵的全局和同时测试制定了推论程序。我们首先开发了一种新的稀疏期望最大化算法来估计模型参数，并仔细地表征了它们的估计精度。然后，在适当的偏置和方差校正后，我们构建一个高斯矩阵，从中我们得出了测试统计信息。最后，我们制定测试程序并建立其渐近保证。我们通过密集的模拟研究了测试的有限样本性能，并用大脑连接分析示例说明了测试。
High-dimensional vector autoregression with measurement error is frequently encountered in a large variety of scientific and business applications. In this article, we study statistical inference of the transition matrix under this model. While there has been a large body of literature studying sparse estimation of the transition matrix, there is a paucity of inference solutions, especially in the high-dimensional scenario. We develop inferential procedures for both the global and simultaneous testing of the transition matrix. We first develop a new sparse expectation-maximization algorithm to estimate the model parameters, and carefully characterize their estimation precisions. We then construct a Gaussian matrix, after proper bias and variance corrections, from which we derive the test statistics. Finally, we develop the testing procedures and establish their asymptotic guarantees. We study the finite-sample performance of our tests through intensive simulations, and illustrate with a brain connectivity analysis example.
