The Annals of Statistics

Statistical estimation for multiplicative cascades

Mina Ossiander and Edward C. Waymire

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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.

Article information

Ann. Statist., Volume 28, Number 6 (2000), 1533-1560.

First available in Project Euclid: 12 March 2002

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Zentralblatt MATH identifier

Primary: 62F20 60F05: Central limit and other weak theorems 60F10: Large deviations 60G57: Random measures 60K40: Other physical applications of random processes
Secondary: 60E10: Characteristic functions; other transforms 60G85

Cascade scaling exponent estimator confidence interval martingale


Ossiander, Mina; Waymire, Edward C. Statistical estimation for multiplicative cascades. Ann. Statist. 28 (2000), no. 6, 1533--1560. doi:10.1214/aos/1015957469.

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