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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.
| Publication type | Article |
|---|---|
| Publication Subtype | Journal Article |
| Title | Estimation of Renyi exponents in random cascades |
| Series title | Bernoulli |
| Volume | 5 |
| Issue | 2 |
| Year Published | 1999 |
| Language | English |
| Publisher | Bernoulli Society for Mathematical Statistics and Probability |
| Description | 17 p. |
| First page | 191 |
| Last page | 207 |
| Online Only (Y/N) | N |
| Additional Online Files (Y/N) | N |
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