We study whether an auctioneer who has only partial knowledge of the distribution of
buyers' valuations can extract the full surplus. There is a finite number of possible
distributions, and the auctioneer has access to a finite number of samples (independent
draws) from the true distribution. Full surplus extraction is possible if the number of samples
is at least the difference between the number of distributions and the dimension of the linear
space they span, plus one. This bound is tight. The mechanism that extracts the full surplus …