Monotonicity-constrained nonparametric estimation and inference for first-price auctions

In the independent private values framework for first-price auctions, we propose a new nonparametric estimator of the probability density of latent valuations that imposes the monotonicity constraint on the estimated inverse bidding strategy. We show that our estimator has a smaller asymptotic variance than that of Guerre, Perrigne and Vuong's estimator. In addition to establishing pointwise asymptotic normality of our estimator, we provide a bootstrap-based approach to constructing uniform confidence bands for the density function.

Automated summary

This study introduces a new nonparametric estimator for estimating the probability density of latent valuations in first-price auctions, which imposes the monotonicity constraint on the estimated inverse bidding strategy. The estimator shows a smaller asymptotic variance compared to previous methods, and a bootstrap-based approach is provided to construct uniform confidence bands for the density function.