Statistical results for the multifractal formalism based on the $S^\nu$ spaces

Computing the spectrum of singularities of a real-life signal by using the definition is impossible. One rather uses an indirect way to compute it: the multifractal formalism. The first multifractal formalism was introduced in the context of fully developped turbulence (1985). Its main default is that it always leads to a concave spectrum. For this reason, the Snu spaces were introduced (2004). They lead to a new multifractal formalism which can detect non concave spectra. In practice, one has to avoid the concept of limit and to deal with finite size effects. We present a method to determine the spectrum based on the Snu spaces and show its statistical efficiency on theoretical some functions and processes.