Simple nonparametric inference for first-price auctions via bid spacings

Abstract

In a classic model of the first-price auction, we propose a nonparametric estimator of the quantile function of bidders' valuations, based on weighted bid spacings. We derive the Bahadur-Kiefer expansion of this estimator with a pivotal influence function and an explicit uniform remainder rate. This expansion allows us to develop a simple algorithm for the associated uniform confidence bands that does not rely on bootstrap. Monte Carlo experiments show satisfactory statistical and computational performance of the estimator and the confidence bands. Estimation and inference for related functionals is also considered.