  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.

Methodology;Applications;Computation