We haw shown how it is relatively powerful to adopts IFS technique in distribution function estimation and related quanties (density and Fourier transform). There are several open issues about the estimators themselves.
The main open problem is about a better characterization of the fixed points of the IFS in order to establish non asymptotic properties for the estimators. The second, and commonly not discussed in the IFS literature, is the problem of choosing the maps w.
There recently appeared some papers that discuss the relationships of some class of IFS and wavelets analysis as well as some papers on local IFS (possible candidates to density functions approximators) but the results there in are not directly useful to statistics.
Stefano M. Iacus, Davide La Torre