Dümbgen, Lutz; Del ConteZerial, Perla (1 March 2013). On lowdimensional projections of highdimensional distributions. In: From Probability to Statistics and Back: HighDimensional Models and Processes. A Festschrift in Honor of Jon Wellner. IMS Collections: Vol. 9 (pp. 91104). Hayward, California: Institute of Mathematical Statistics 10.1214/12IMSCOLL908

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Let P be a probability distribution on q dimensional space. The socalled DiaconisFreedman effect means that for a fixed dimension d<<q , most d dimensional projections of P look like a scale mixture of spherically symmetric Gaussian distributions. The present paper provides necessary and sufficient conditions for this phenomenon in a suitable asymptotic framework with increasing dimension q . It turns out, that the conditions formulated by Diaconis and Freedman (1984) are not only sufficient but necessary as well. Moreover, letting P ^ be the empirical distribution of n independent random vectors with distribution P , we investigate the behavior of the empirical process n √ (P ^ −P) under random projections, conditional on P ^ .
Item Type: 
Conference or Workshop Item (Paper) 

Division/Institute: 
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science 
UniBE Contributor: 
Dümbgen, Lutz 
Subjects: 
500 Science > 510 Mathematics 
ISSN: 
19394039 
ISBN: 
9780940600836 
Series: 
IMS Collections 
Publisher: 
Institute of Mathematical Statistics 
Language: 
English 
Submitter: 
Lutz Dümbgen 
Date Deposited: 
12 Mar 2014 08:44 
Last Modified: 
07 Dec 2014 08:22 
Publisher DOI: 
10.1214/12IMSCOLL908 
BORIS DOI: 
10.7892/boris.41510 
URI: 
https://boris.unibe.ch/id/eprint/41510 