From Low- to High-Dimensional Moments Without Magic

Bernhard G. Bodmann (), Martin Ehler () and Manuel Gräf ()
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Bernhard G. Bodmann: University of Houston
Martin Ehler: University of Vienna
Manuel Gräf: Austrian Academy of Sciences

Journal of Theoretical Probability, 2018, vol. 31, issue 4, 2167-2193

Abstract: 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.

Keywords: High-dimensional moments; Random matrices; Orthogonal projections; Zonal polynomials; 44A60; 42C15; 42C05 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s10959-017-0785-x

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