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.
Document type: | Working paper |
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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 > Institut für Mathematik |
DDC-classification: | 510 Mathematics |
Series: | Beiträge zur Statistik > Reports |