Approximation of Projections of Random Vectors

Elizabeth Meckes ()
Additional contact information
Elizabeth Meckes: Case Western Reserve University

Journal of Theoretical Probability, 2012, vol. 25, issue 2, 333-352

Abstract: Abstract Let X be a d-dimensional random vector and X θ its projection onto the span of a set of orthonormal vectors {θ 1,…,θ k }. Conditions on the distribution of X are given such that if θ is chosen according to Haar measure on the Stiefel manifold, the bounded-Lipschitz distance from X θ to a Gaussian distribution is concentrated at its expectation; furthermore, an explicit bound is given for the expected distance, in terms of d, k, and the distribution of X, allowing consideration not just of fixed k but of k growing with d. The results are applied in the setting of projection pursuit, showing that most k-dimensional projections of n data points in ℝ d are close to Gaussian, when n and d are large and k=clog (d) for a small constant c.

Keywords: Random measures; Projection pursuit; Entropy; Measure concentration; Stein’s method; 60G57; 60E15; 62E20 (search for similar items in EconPapers)
Date: 2012
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s10959-010-0299-2 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:jotpro:v:25:y:2012:i:2:d:10.1007_s10959-010-0299-2

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/10959

DOI: 10.1007/s10959-010-0299-2

Access Statistics for this article

Journal of Theoretical Probability is currently edited by Andrea Monica

More articles in Journal of Theoretical Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().