Unbiased estimation of multi-fractal dimensions of finite data sets

Abstract

We present a novel method for determining multi-fractal properties from experimental data. It is based on maximising the likelihood that the given finite data set comes from a particular set of parameters in a multi-parameter family of well known multi-fractals. By comparing characteristic correlations obtained from the original data with those that occur in artificially generated multi-fractals with the {\em same} number of data points, we expect that predicted multi-fractal properties are unbiased by the finiteness of the experimental data.