Detail
On conditional moments of high-dimensional random vectors given lower-dimensional projections
- Author(s)
- Lukas Steinberger, Hannes Leeb
- Abstract
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).
- Organisation(s)
- Department of Statistics and Operations Research, Research Network Data Science
- Journal
- Bernoulli: a journal of mathematical statistics and probability
- Volume
- 24
- Pages
- 565–591
- No. of pages
- 27
- ISSN
- 1350-7265
- DOI
- https://doi.org/10.3150/16-BEJ888
- Publication date
- 02-2018
- Peer reviewed
- Yes
- Austrian Fields of Science 2012
- 101018 Statistics
- Keywords
- ASJC Scopus subject areas
- Statistics and Probability
- Portal url
- https://ucris.univie.ac.at/portal/en/publications/on-conditional-moments-of-highdimensional-random-vectors-given-lowerdimensional-projections(553a308c-256a-47eb-bd79-a12f77496d69).html