具有测量误差的高维向量自回归的统计推断

IF 1.5 3区 数学 Q2 STATISTICS & PROBABILITY
Xiang Lyu, Jian Kang, Lexin Li
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引用次数: 0

摘要

具有测量误差的高维向量自回归在各种科学和商业应用中经常遇到。在本文中,我们研究了在这个模型下转移矩阵的统计推断。虽然有大量文献研究转移矩阵的稀疏估计,但推理解决方案很少,尤其是在高维场景中。我们为转移矩阵的全局和同时测试开发了推理程序。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,并仔细描述了它们的估计精度。然后,经过适当的偏差和方差校正,我们构造了一个高斯矩阵,从中我们得出了测试统计数据。最后,我们开发了测试程序,并建立了它们的渐近保证。我们通过深入的模拟研究了测试的有限样本性能,并以大脑连接分析为例进行了说明。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error.

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.

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来源期刊
Statistica Sinica
Statistica Sinica 数学-统计学与概率论
CiteScore
2.10
自引率
0.00%
发文量
82
审稿时长
10.5 months
期刊介绍: Statistica Sinica aims to meet the needs of statisticians in a rapidly changing world. It provides a forum for the publication of innovative work of high quality in all areas of statistics, including theory, methodology and applications. The journal encourages the development and principled use of statistical methodology that is relevant for society, science and technology.
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