Statistical estimation for multiplicative cascades

• 成果类型: Article
• 署名作者: Ossiander, M; Waymire, EC
• 署名单位: Oregon State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2000
• 页码: 1533-1560
• 关键词: fully-developed turbulence; independent random cascades; log-poisson statistics; exponents

摘要

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.