  In this paper, we prove central limit theorems for bias reduced estimators of
the structure function of several multifractal processes, namely mutiplicative
cascades, multifractal random measures, multifractal random walk and
multifractal fractional random walk as defined by Lude\~{n}a [Ann. Appl.
Probab. 18 (2008) 1138-1163]. Previous estimators of the structure functions
considered in the literature were severely biased with a logarithmic rate of
convergence, whereas the estimators considered here have a polynomial rate of
convergence.
