Estimation and inference of seller’s expected revenue in first-price auctions

I propose an estimator for the seller’s expected revenue function in a first-price sealed-bid auction with independent private values and symmetric bidders, who can exhibit constant relative risk aversion and bid according to the Bayesian Nash equilibrium. I build the proposed estimator from pseudo-private values, which can be estimated from observed bids, and show that it is pointwise and uniformly consistent: the corresponding optimal nonparametric rates of convergence can be achieved. Then I construct asymptotically valid confidence intervals and uniform confidence bands. Suggestions for critical values are based on first-order asymptotics, as well as on the bootstrap method.