  We consider inference on the probability density of valuations in the
first-price sealed-bid auctions model within the independent private value
paradigm. We show the asymptotic normality of the two-step nonparametric
estimator of Guerre, Perrigne, and Vuong (2000) (GPV), and propose an easily
implementable and consistent estimator of the asymptotic variance. We prove the
validity of the pointwise percentile bootstrap confidence intervals based on
the GPV estimator. Lastly, we use the intermediate Gaussian approximation
approach to construct bootstrap-based asymptotically valid uniform confidence
bands for the density of the valuations.
