Nonparametric Quantile Density Estimation and Structural
Analysis of First-Price Auctions
Nonparametric estimators of the quantile density function
(the derivative of the quantile function): kernel, boundary-corrected
kernel, Poisson-weight and Bernstein-polynomial smoothers, indirect
estimators (Jones (1992)
< https://www.ism.ac.jp/editsec/aism/pdf/044_4_0721.pdf>; Soni, Dewan and
Jain (2012) ; Chaubey, Dewan and Li (2024)
), and linear, hard-thresholded and
block-thresholded wavelet estimators (Chesneau, Dewan and Doosti (2016)
; Shirazi and Doosti (2022)
), with smoothing parameters chosen by
biased, robust likelihood (Wu (2019) )
or least-squares cross-validation. The estimators are applied to the
structural analysis of first-price sealed-bid auctions: recovery of
private values for independent or affiliated values and risk-neutral or
risk-averse bidders (Doosti, Dewan and Talebian (2025)
; Doosti (2026)
), estimation of the private-value
density with kernel benchmarks (Hickman and Hubbard (2015)
; Marmer and Shneyerov (2012)
; Zincenko (2024)
) and confidence bands (Ma, Marmer and
Shneyerov (2019) ), and estimation of
the seller's expected revenue and optimal reserve price, with tools for
simulating equilibrium bids and comparing estimators.