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{1015957469,
author = {Ossiander, Mina and Waymire, Edward C.},
title = {Statistical estimation for multiplicative cascades},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 1533-1560},
language = {en},
url = {http://dml.mathdoc.fr/item/1015957469}
}
Ossiander, Mina; Waymire, Edward C. Statistical estimation for multiplicative cascades. Ann. Statist., Tome 28 (2000) no. 3, pp. 1533-1560. http://gdmltest.u-ga.fr/item/1015957469/