Back To Index Previous Article Next Article Full Text

Statistica Sinica 33 (2023), 1435-1459

STATISTICAL INFERENCE FOR
HIGH-DIMENSIONAL VECTOR AUTOREGRESSION
WITH MEASUREMENT ERROR

Xiang Lyu1, Jian Kang2 and Lexin Li1

1University of California at Berkeley and 2University of Michigan

Abstract: High-dimensional vector autoregressions with measurement errors are frequently encountered in scientific and business applications. We study the statistical inference of the transition matrix under such models. Although numerous works have examined sparse estimations of the transition matrix, relative few provide inference solutions, especially in the high-dimensional setting. We study both 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 the estimation precision. Next, we construct a Gaussian matrix, after proper bias and variance corrections, from which we derive the test statistics. Then, we develop the test procedures and establish their asymptotic guarantees. Finally, we use simulations to investigate performance of our tests, and apply the tests to a neuroimaging-based brain connectivity analysis.

Key words and phrases: Brain network analysis, covariance inference, expectation-maximization, global testing, simultaneous testing, vector autoregression.

Back To Index Previous Article Next Article Full Text