- Volume 5, Number 2 (1999), 191-207.
Estimation of Rényi exponents in random cascades
We consider statistical estimation of the Rényi exponent , which characterizes the scaling behaviour of a singular measure defined on a subset of . The Rényi exponent is defined to be , assuming that this limit exists, where and, for , are the cubes of a -coordinate mesh that intersect the support of . In particular, we demonstrate asymptotic normality of the least-squares estimator of 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.
Bernoulli, Volume 5, Number 2 (1999), 191-207.
First available in Project Euclid: 5 March 2007
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Troutman, Brent M.; Vecchia, Aldo V. Estimation of Rényi exponents in random cascades. Bernoulli 5 (1999), no. 2, 191--207. https://projecteuclid.org/euclid.bj/1173147902