A note on random densities via wavelets

It is a well-known fact that any orthonormal basis in L2 can produce a "random density". If {[phi]n} is an orthonormal basis and {an} is a sequence of random variables such that [Sigma] an2 = 1 a.s., then [latin small letter f with hook](x) = [Sigma] an[phi]n(x)2 is a random density. In this note we define a random density via orthogonal bases of wavelets and explore some of its basic properties.

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Year of publication:	1996
Authors:	Vidakovic, Brani
Published in:	Statistics & Probability Letters. - Elsevier, ISSN 0167-7152. - Vol. 26.1996, 4, p. 315-321
Publisher:	Elsevier
Subject:	Wavelets Parseval's identity Random density

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Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10005224170