  Solar explosive events are commonly explained as small scale magnetic
reconnection events, although unambiguous confirmation of this scenario remains
elusive due to the lack of spatial resolution and of the statistical analysis
of large enough samples of this type of events. In this work, we propose a
sound statistical treatment of data cubes consisting of a temporal sequence of
long slit spectra of the solar atmosphere. The analysis comprises all the
stages from the explosive event detection to its characterization and the
subsequent sample study. We have designed two complementary approaches based on
the combination of standard statistical techniques (Robust Principal Component
Analysis in one approach and wavelet decomposition and Independent Component
Analysis in the second) in order to obtain least biased samples. These
techniques are implemented in the spirit of letting the data speak for
themselves. The analysis is carried out for two spectral lines: the C IV line
at 1548.2 angstroms and the Ne VIII line at 770.4 angstroms. We find
significant differences between the characteristics of the line profiles
emitted in the proximities of two active regions, and in the quiet Sun, most
visible in the relative importance of a separate population of red shifted
profiles. We also find a higher frequency of explosive events near the active
regions, and in the C IV line. The distribution of the explosive events
characteristics is interpreted in the light of recent numerical simulations.
Finally, we point out several regions of the parameter space where the
reconnection model has to be refined in order to explain the observations.
