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From Low- to High-Dimensional Moments Without Magic

Author

Listed:
  • Bernhard G. Bodmann

    (University of Houston)

  • Martin Ehler

    (University of Vienna)

  • Manuel Gräf

    (Austrian Academy of Sciences)

Abstract

We aim to compute the first few moments of a high-dimensional random vector from the first few moments of a number of its low-dimensional projections. To this end, we identify algebraic conditions on the set of low-dimensional projectors that yield explicit reconstruction formulas. We also provide a computational framework, with which suitable projectors can be derived by solving an optimization problem. Finally, we show that randomized projections permit approximate recovery.

Suggested Citation

  • Bernhard G. Bodmann & Martin Ehler & Manuel Gräf, 2018. "From Low- to High-Dimensional Moments Without Magic," Journal of Theoretical Probability, Springer, vol. 31(4), pages 2167-2193, December.
    • Handle: RePEc:spr:jotpro:v:31:y:2018:i:4:d:10.1007_s10959-017-0785-x
    DOI: 10.1007/s10959-017-0785-x
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    References listed on IDEAS

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    1. Juan Antonio Cuesta-Albertos & Ricardo Fraiman & Thomas Ransford, 2007. "A Sharp Form of the Cramér–Wold Theorem," Journal of Theoretical Probability, Springer, vol. 20(2), pages 201-209, June.
    2. Roman Vershynin, 2012. "How Close is the Sample Covariance Matrix to the Actual Covariance Matrix?," Journal of Theoretical Probability, Springer, vol. 25(3), pages 655-686, September.
    3. Minsker, Stanislav, 2017. "On some extensions of Bernstein’s inequality for self-adjoint operators," Statistics & Probability Letters, Elsevier, vol. 127(C), pages 111-119.
    Full references (including those not matched with items on IDEAS)

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