| 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. |
| Genre: | Article |
| ProdID: | 70021005 |
| Citation Author: | Troutman, B. M.; Vecchia, A. V. |
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| Citation End Page: | 207 |
| Citation Issue: | 2 |
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| Citation Language: | English |
| Citation Larger Work Title: | Bernoulli |
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| Citation Number Of Pages: | 17 |
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| Citation Search Results Text: | Estimation of Re??nyi exponents in random cascades; 1999; Article; Journal; Bernoulli; Troutman, B. M.; Vecchia, A. V. |
| Citation Start Page: | 191 |
| Citation Volume: | 5 |
| Citation Year: | 1999 |
| Type: | citation/reference |
| Text: | Estimation of Re??nyi exponents in random cascades; 1999; Article; Journal; Bernoulli; Troutman, B. M.; Vecchia, A. V. |
| URL (THUMBNAIL): | http://pubs.er.usgs.gov/thumbnails/outside_thumb.jpg |
| Date Other: | Fri, 1 Jan 1999 00:00 -0600 |
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