  We provide efficient estimation methods for first- and second-price auctions
under independent (asymmetric) private values and partial observability. Given
a finite set of observations, each comprising the identity of the winner and
the price they paid in a sequence of identical auctions, we provide algorithms
for non-parametrically estimating the bid distribution of each bidder, as well
as their value distributions under equilibrium assumptions. We provide
finite-sample estimation bounds which are uniform in that their error rates do
not depend on the bid/value distributions being estimated. Our estimation
guarantees advance a body of work in Econometrics wherein only identification
results have been obtained, unless the setting is symmetric, parametric, or all
bids are observable. Our guarantees also provide computationally and
statistically effective alternatives to classical techniques from reliability
theory. Finally, our results are immediately applicable to Dutch and English
auctions.
