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Testing unconditional and conditional independence via mutual information

Author

Listed:
  • Ai, Chunrong
  • Sun, Li-Hsien
  • Zhang, Zheng
  • Zhu, Liping

Abstract

Testing independence has garnered increasing attention in the econometric and statistical literature. Many tests have been proposed, most of which are inconsistent against all departures from independence. Few of those tests, though consistent, suffer a significant loss of local power. This study proposes a mutual information test for testing independence. The proposed test is simple to implement and, with a slight loss of local power, is consistent against all departures from independence. The key driving factor is that we estimate the density ratio directly. This value is constant in a state of independence. This is in contrast with related studies that estimate the joint and marginal density functions to form the density ratio. A small-scale simulation study indicates that the proposed test outperforms the existing alternatives in various dependence structures.

Suggested Citation

  • Ai, Chunrong & Sun, Li-Hsien & Zhang, Zheng & Zhu, Liping, 2024. "Testing unconditional and conditional independence via mutual information," Journal of Econometrics, Elsevier, vol. 240(2).
    • Handle: RePEc:eee:econom:v:240:y:2024:i:2:s0304407622001609
    DOI: 10.1016/j.jeconom.2022.07.011
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    Keywords

    Convex optimization; Density ratio; Independence test; Mutual information;
    All these keywords.

    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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