Nonparametric estimation of first price auctions via density-quantile function

We propose a nonparametric estimator of bidders' value function based on a kernel estimator of the density-quantile function of bids in first price auctions. This estimator provides certain advantage over the conventional approach that relies on the distribution/density ratio of the bids. We use a boundary-adaptive kernel for boundary bias correction and propose a practical method of bandwidth selection. Our numerical experiments demonstrate good performance of the proposed method in the estimation of first price auctions with risk neutral and risk averse bidders. (C) 2022 Elsevier B.V. All rights reserved.