  In the 70s a novel branch of statistics emerged focusing its effort in
selecting a function in the pattern recognition problem, which fulfils a
definite relationship between the quality of the approximation and its
complexity. These data-driven approaches are mainly devoted to problems of
estimating dependencies with limited sample sizes and comprise all the
empirical out-of sample generalization approaches, e.g. cross validation (CV)
approaches. Although the latter are \emph{not designed for testing competing
hypothesis or comparing different models} in neuroimaging, there are a number
of theoretical developments within this theory which could be employed to
derive a Statistical Agnostic (non-parametric) Mapping (SAM) at voxel or
multi-voxel level. Moreover, SAMs could relieve i) the problem of instability
in limited sample sizes when estimating the actual risk via the CV approaches,
e.g. large error bars, and provide ii) an alternative way of Family-wise-error
(FWE) corrected p-value maps in inferential statistics for hypothesis testing.
In this sense, we propose a novel framework in neuroimaging based on
concentration inequalities, which results in (i) a rigorous development for
model validation with a small sample/dimension ratio, and (ii) a
less-conservative procedure than FWE p-value correction, to determine the brain
significance maps from the inferences made using small upper bounds of the
actual risk.
