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Estimation of Re??nyi exponents in random cascades

Bernoulli

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Abstract

We consider statistical estimation of the Re??nyi exponent ??(h), which characterizes the scaling behaviour of a singular measure ?? defined on a subset of Rd. The Re??nyi exponent is defined to be lim?????0 [{log M??(h)}/(-log ??)], assuming that this limit exists, where M??(h) = ??i??h(??i) and, for ??>0, {??i} are the cubes of a ??-coordinate mesh that intersect the support of ??. In particular, we demonstrate asymptotic normality of the least-squares estimator of ??(h) when the measure ?? is generated by a particular class of multiplicative random cascades, a result which allows construction of interval estimates and application of hypothesis tests for this scaling exponent. Simulation results illustrating this asymptotic normality are presented. ?? 1999 ISI/BS.

Additional Publication Details

Publication type:
Article
Publication Subtype:
Journal Article
Title:
Estimation of Re??nyi exponents in random cascades
Series title:
Bernoulli
Volume
5
Issue:
2
Year Published:
1999
Language:
English
Larger Work Type:
Article
Larger Work Subtype:
Journal Article
First page:
191
Last page:
207
Number of Pages:
17