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.
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