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It is well known that non-parametric methods suffer from the "curse ofdimensionality". We propose here a new estimation method for a multivariatedistribution, using sub-sampling and ranks, which seems not to suffer from this"curse". We prove that in case of independence, the uncertainty of theestimated distribution increases almost linearly w.r.t. the dimension, fordimensions around 6. Otherwise, a simulation study shows that if we use thisestimation to build an independence test, the number of observations needed toobtain a given power increases linearly with the dimension. Finally, we giveexamples of a regression using this estimation: with 3000 observations, indimension 5, with a markedly complicated dependence, the estimated distributionis graphically very similar to the real one.

Estimate dependence in medium dimensions, using ranks and sub-sampling