Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error
Abstract
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.
Cite
@article{arxiv.2009.08011,
title = {Statistical Inference for High-Dimensional Vector Autoregression with Measurement Error},
author = {Xiang Lyu and Jian Kang and Lexin Li},
journal= {arXiv preprint arXiv:2009.08011},
year = {2020}
}