Open Access
February 2018 On conditional moments of high-dimensional random vectors given lower-dimensional projections
Lukas Steinberger, Hannes Leeb
Bernoulli 24(1): 565-591 (February 2018). DOI: 10.3150/16-BEJ888


One of the most widely used properties of the multivariate Gaussian distribution, besides its tail behavior, is the fact that conditional means are linear and that conditional variances are constant. We here show that this property is also shared, in an approximate sense, by a large class of non-Gaussian distributions. We allow for several conditioning variables and we provide explicit non-asymptotic results, whereby we extend earlier findings of Hall and Li (Ann. Statist. 21 (1993) 867–889) and Leeb (Ann. Statist. 41 (2013) 464–483).


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Lukas Steinberger. Hannes Leeb. "On conditional moments of high-dimensional random vectors given lower-dimensional projections." Bernoulli 24 (1) 565 - 591, February 2018.


Received: 1 June 2014; Revised: 1 June 2016; Published: February 2018
First available in Project Euclid: 27 July 2017

zbMATH: 06778340
MathSciNet: MR3706769
Digital Object Identifier: 10.3150/16-BEJ888

Keywords: Conditional moments , constant conditional variance , high dimensional distribution , linear conditional mean

Rights: Copyright © 2018 Bernoulli Society for Mathematical Statistics and Probability

Vol.24 • No. 1 • February 2018
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