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December2000 Statistical estimation for multiplicative cascades
Mina Ossiander, Edward C. Waymire
Ann. Statist. 28(6): 1533-1560 (December2000). DOI: 10.1214/aos/1015957469

Abstract

The probability distribution of the cascade generators in a random multiplicative cascade represents a hidden parameter which is reflected in the fine scale limiting behavior of the scaling exponents (sample moments) of a single sample cascade realization as a.s.constants.We identify a large class of cascade generators uniquely determined by these scaling exponents. For this class we provide both asymptotic consistency and confidence intervals for two different estimators of the cumulant generating function (log Laplace transform) of the cascade generator distribution. These results are derived from investigation of the convergence properties of the fine scale sample moments of a single cascade realization.

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Mina Ossiander. Edward C. Waymire. "Statistical estimation for multiplicative cascades." Ann. Statist. 28 (6) 1533 - 1560, December2000. https://doi.org/10.1214/aos/1015957469

Information

Published: December2000
First available in Project Euclid: 12 March 2002

zbMATH: 1105.60305
MathSciNet: MR1835030
Digital Object Identifier: 10.1214/aos/1015957469

Subjects:
Primary: 60F05 , 60F10 , 60G57 , 60K40 , 62F20
Secondary: 60E10 , 60G85

Keywords: Cascade , Confidence interval , estimator , martingale , Scaling exponent

Rights: Copyright © 2000 Institute of Mathematical Statistics

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Vol.28 • No. 6 • December2000
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