Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error
Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error
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DOI：
10.5705/ss.202021.0151
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发表时间：
2020-09
影响因子：
1.4
通讯作者：
Xiang Lyu;Jian Kang;Lexin Li
中科院分区：
文献类型：
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作者：
Xiang Lyu;Jian Kang;Lexin Li
在科学和商业应用中，经常会遇到带有测量误差的高维向量自回归。本文研究了该模型下转移矩阵的统计推断。虽然已经有大量的文献研究稀疏估计的转移矩阵，有一个推理解决方案，特别是在高维的情况下，缺乏。我们开发的推理程序的过渡矩阵的全球和同时测试。我们首先提出一种新的稀疏期望最大化算法来估计模型参数，并仔细地描述了它们的估计精度。然后，我们构造一个高斯矩阵，经过适当的偏差和方差校正，从中我们得到的测试统计量。最后，我们开发的测试程序，并建立其渐近保证。我们通过密集的模拟来研究我们的测试的有限样本性能，并以大脑连接分析为例进行说明。
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.