This paper proposes a nonparametric estimator for the bidders’ utility function and the density of private values in a first-price sealed-bid auction model. Specifically, I study a setting with risk-averse bidders within the independent private value paradigm. I adopt a fully nonparametric approach by not placing any restrictions on the shape of the bidders’ utility function beyond strict monotonicity, concavity, and differentiability. In contrast to previous literature, I characterize such utility function and the density of private values by a minimizer of a certain functional. I estimate this minimizer, which is a smooth real-valued function, in two steps by the method of sieves. Then, the estimators for the bidders’ utility function and the density of private values are smooth functionals of the estimator for the minimizer. The estimator for the utility function is uniformly consistent and shape-preserving, while the estimator for the density is uniformly consistent and asymptotically normal. Monte Carlo experiments suggest that the proposed estimators have good finite sample properties, and also, an application to the US Forest Service timber auctions is provided. JEL Classification: C14, D44.