Large area lensing surveys are expected to make it possible to use cosmic shear tomography as a tool to severely constrain cosmological parameters. To this end, one typically relies on second order statistics such as the two - point correlation fucntion and its Fourier counterpart, the power spectrum. Moving a step forward, we wonder whether and to which extent higher order stastistics can improve the lensing Figure of Merit (FoM). In this first paper of a series, we investigate how second, third and fourth order lensing convergence moments can be measured and use as probe of the underlying cosmological model. We use simulated data and investigate the impact on moments estimate of the map reconstruction procedure, the cosmic variance, and the intrinsic ellipticity noise. We demonstrate that, under realistic assumptions, it is indeed possible to use higher order moments as a further lensing probe.
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