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July 2011 Approximating the moments of marginals of high-dimensional distributions
Roman Vershynin
Ann. Probab. 39(4): 1591-1606 (July 2011). DOI: 10.1214/10-AOP589


For probability distributions on ℝn, we study the optimal sample size N = N(n, p) that suffices to uniformly approximate the pth moments of all one-dimensional marginals. Under the assumption that the marginals have bounded 4p moments, we obtain the optimal bound N = O(np/2) for p > 2. This bound goes in the direction of bridging the two recent results: a theorem of Guedon and Rudelson [Adv. Math. 208 (2007) 798–823] which has an extra logarithmic factor in the sample size, and a result of Adamczak et al. [J. Amer. Math. Soc. 23 (2010) 535–561] which requires stronger subexponential moment assumptions.


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Roman Vershynin. "Approximating the moments of marginals of high-dimensional distributions." Ann. Probab. 39 (4) 1591 - 1606, July 2011.


Published: July 2011
First available in Project Euclid: 5 August 2011

zbMATH: 1271.62122
MathSciNet: MR2857251
Digital Object Identifier: 10.1214/10-AOP589

Primary: 62H12
Secondary: 46B09 , 60B20

Keywords: heavy-tailed distributions , High-dimensional distributions , marginals , random matrices , statistical estimation

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 4 • July 2011
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