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A Projection-based Conditional Dependence Measure with Applications to High-dimensional Undirected Graphical Models.

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A novel projection-based method measures conditional dependence in econometrics, enabling efficient conditional independence testing even with many factors. This approach facilitates building dependency graphs without Gaussian assumptions, outperforming existing methods.

Keywords:
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Area of Science:

  • Econometrics
  • Graphical Models
  • Statistical Inference

Background:

  • Conditional dependence measurement is crucial in econometrics and graphical models.
  • Existing methods may face limitations in high-dimensional factor settings.

Purpose of the Study:

  • To propose a new projection-based measure for conditional dependence.
  • To develop an efficient conditional independence test with controllable Type I error.
  • To establish a method for constructing dependency graphs without Gaussian assumptions.

Main Methods:

  • A novel projection-based conditional dependence measure is introduced.
  • A conditional independence test is developed, analyzing its asymptotic null distribution.
  • A generic graph-building method is elaborated using the new test.

Main Results:

  • The new conditional independence test demonstrates control over asymptotic Type I error.
  • The test is computationally efficient, even in high-dimensional factor scenarios.
  • Simulations and real data studies confirm the superiority of the proposed method.

Conclusions:

  • The new projection-based method offers a robust approach for measuring conditional dependence.
  • The developed test and graph-building technique are valuable for econometrics and graphical modeling.
  • The R package pgraph implements this superior methodology for practical applications.