Estimation of Renyi exponents in random cascades
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.
Citation Information
Publication Year | 1999 |
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Title | Estimation of Renyi exponents in random cascades |
Authors | Brent M. Troutman, Aldo V. Vecchia |
Publication Type | Article |
Publication Subtype | Journal Article |
Series Title | Bernoulli |
Index ID | 70021005 |
Record Source | USGS Publications Warehouse |