Estimation of Exchangeable Distribution with Order Statistics: Application to First-Price Auctions

Abstract

This study examines the estimation of the exchangeable joint distribution when the highest (lowest) and another order statistics are observable. The estimator would be appropriate for the estimation of the valuation distribution of auctions and "order-biased" sampling, such as school student achievement investigations, when the sampling probability is not completely captured by the observed covariates. We present our method in conjunction with an application for a first-price sealed-bid auction with affiliation. The results potentially extend the existing non-parametric identification result for first-price sealed-bid auctions with symmetric affiliation.