Bernoulli

  • Bernoulli
  • Volume 5, Number 2 (1999), 191-207.

Estimation of Rényi exponents in random cascades

Brent M. Troutman and Aldo V. Vecchia

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Abstract

We consider statistical estimation of the Rényi exponent τ (h) , which characterizes the scaling behaviour of a singular measure μ defined on a subset of R d . The Rényi exponent is defined to be lim δ 0 [{logM δ (h)}/(-logδ)] , assuming that this limit exists, where M δ (h)= i μ h(Δ i) and, for δ >0 , { Δ i} are the cubes of a δ -coordinate mesh that intersect the support of μ . In particular, we demonstrate asymptotic normality of the least-squares estimator of τ (h) when the measure μ 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.

Article information

Source
Bernoulli, Volume 5, Number 2 (1999), 191-207.

Dates
First available in Project Euclid: 5 March 2007

Permanent link to this document
https://projecteuclid.org/euclid.bj/1173147902

Mathematical Reviews number (MathSciNet)
MR1681694

Zentralblatt MATH identifier
0953.62088

Keywords
least-squares estimation multifractal multiplicative process random cascade Rényi exponent scaling exponent

Citation

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


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