Lyu Xiang, Kang Jian, Li Lexin
University of California at Berkeley.
University of Michigan.
Stat Sin. 2023 May;33(Spec Issue):1435-1459. doi: 10.5705/ss.202021.0151.
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.
带有测量误差的高维向量自回归在各种各样的科学和商业应用中经常遇到。在本文中，我们研究该模型下转移矩阵的统计推断。虽然已有大量文献研究转移矩阵的稀疏估计，但推断解决方案却很少，尤其是在高维情况下。我们开发了用于转移矩阵全局和同时检验的推断程序。我们首先开发一种新的稀疏期望最大化算法来估计模型参数，并仔细刻画它们的估计精度。然后，经过适当的偏差和方差校正后，我们构造一个高斯矩阵，从中导出检验统计量。最后，我们开发检验程序并建立其渐近保证。我们通过大量模拟研究了我们检验的有限样本性能，并以一个脑连接性分析示例进行了说明。
