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Summary
This summary is machine-generated.

This study introduces new statistical inference methods for high-dimensional vector autoregression with measurement error. The developed procedures enable robust testing of the transition matrix, crucial for complex scientific and business data analysis.

Keywords:
Brain connectivity analysisCovariance inferenceExpectation-maximization algorithmGlobal testingSimultaneous testingVector autoregression

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Area of Science:

  • Statistics
  • Econometrics
  • Machine Learning

Background:

  • High-dimensional vector autoregression with measurement error is common in science and business.
  • Existing research lacks robust inference solutions for this model, particularly in high dimensions.

Purpose of the Study:

  • To develop statistical inference procedures for the transition matrix in high-dimensional vector autoregression with measurement error.
  • To enable both global and simultaneous testing of the transition matrix.

Main Methods:

  • A novel sparse expectation-maximization algorithm for parameter estimation.
  • Construction of a bias- and variance-corrected Gaussian matrix for test statistic derivation.
  • Development of testing procedures with established asymptotic guarantees.

Main Results:

  • Accurate estimation of model parameters with characterized precision.
  • Development of statistically sound inferential procedures for the transition matrix.
  • Demonstrated finite-sample performance through simulations.

Conclusions:

  • The proposed methods provide essential inferential tools for high-dimensional vector autoregression with measurement error.
  • The study addresses a significant gap in statistical inference for complex data models.
  • The approach is validated through simulations and an application in brain connectivity analysis.