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Non-Independent Components Analysis

Author

Listed:
  • Geert Mesters
  • Piotr Zwiernik

Abstract

A seminal result in the ICA literature states that for AY = ? if the components of ? are independent and at most one is Gaussian, then A is identified up to sign and permutation of its rows [Comon, 1994]. In this paper we study to which extent the independence assumption can be relaxed by replacing it with restrictions on higher order moment or cumulant tensors of ?. We document new conditions that establish identification for several non-independent component models, e.g. common variance models, and propose efficient estimation methods based on the identification results. We show that in situations where independence cannot be assumed the efficiency gains can be significant relative to methods that rely on independence.

Suggested Citation

  • Geert Mesters & Piotr Zwiernik, 2022. "Non-Independent Components Analysis," Working Papers 1358, Barcelona School of Economics.
    • Handle: RePEc:bge:wpaper:1358
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    References listed on IDEAS

    as
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    10. David Brillinger, 1969. "The calculation of cumulants via conditioning," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 215-218, December.
    11. Guay, Alain, 2021. "Identification of structural vector autoregressions through higher unconditional moments," Journal of Econometrics, Elsevier, vol. 225(1), pages 27-46.
    12. José Luis Montiel Olea & Mikkel Plagborg-Møller & Eric Qian, 2022. "SVAR Identification from Higher Moments: Has the Simultaneous Causality Problem Been Solved?," AEA Papers and Proceedings, American Economic Association, vol. 112, pages 481-485, May.
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    Cited by:

    1. Martin Bruns & Sascha A. Keweloh, 2023. "Testing for Strong Exogeneity in Proxy-VARS," University of East Anglia School of Economics Working Paper Series 2023-07, School of Economics, University of East Anglia, Norwich, UK..
    2. Cordoni, Francesco & Dorémus, Nicolas & Moneta, Alessio, 2024. "Identification of vector autoregressive models with nonlinear contemporaneous structure," Journal of Economic Dynamics and Control, Elsevier, vol. 162(C).
    3. Sascha A. Keweloh, 2023. "Structural Vector Autoregressions and Higher Moments: Challenges and Solutions in Small Samples," Papers 2310.08173, arXiv.org.

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    More about this item

    Keywords

    independent components analysis; cumulants; moments; tensors; identification;
    All these keywords.

    JEL classification:

    • C20 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - General
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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