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.

中文翻译：

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最高价拍卖中卖方预期收入的估计和推断

我提出了一个估计器，用于在具有独立私人价值和对称投标人的第一价格密封投标拍卖中卖方的预期收入函数，这些投标人可以根据贝叶斯纳什均衡表现出恒定的相对风险厌恶和投标。我根据伪私有值构建了建议的估计器，该估计器可以根据观察到的出价进行估计，并表明它是逐点且一致一致的：可以实现相应的最佳非参数收敛率。然后，我构建渐进有效的置信区间和均匀置信带。临界值的建议基于一阶渐近法以及引导方法。