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Remarks on Low-Dimensional Projections of High-Dimensional Distributions

Dümbgen, Lutz ; Zerial, Perla

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Abstract

Let P be a probability distribution on q-dimensional space. Necessary and sufficient conditions are derived under which a random d-dimensional projection of P converges weakly to a fixed distribution Q as q tends to infinity, while d is an arbitrary fixed number. This complements a well-known result of Diaconis and Freedman (1984). Further we investigate d-dimensional projections of ^P, where ^P is the empirical distribution of a random sample from P of size n. We prove a conditional Central Limit Theorem for random projections of ^P - P given the data ^P, as q and n tend to infinity.

Item Type: Working paper
Place of Publication: Heidelberg
Date Deposited: 01 Jul 2016 07:26
Date: 6 December 1996
Number of Pages: 19
Faculties / Institutes: The Faculty of Mathematics and Computer Science > Department of Applied Mathematics
Subjects: 510 Mathematics
Schriftenreihe ID: Beiträge zur Statistik > Reports
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