Uniform confidence bands in deconvolution with unknown error distribution

Abstract: This paper develops a method to construct uniform confidence bands in deconvolution when the error distribution is unknown. We mainly focus on the baseline setting where an auxiliary sample from the error distribution is available and the error density is ordinary smooth. The auxiliary sample may directly come from validation data, or can be constructed from panel data with a symmetric error distribution. We also present extensions of the results on confidence bands to the case of super-smooth error densities. Simulation studies demonstrate the performance of the multiplier bootstrap confidence band in the finite sample. We apply our method to the Outer Continental Shelf (OCS) Auction Data and draw confidence bands for the density of common values of mineral rights on oil and gas tracts. Finally, we present an application of our main theoretical result specifically to additive fixed-effect panel data models. As an empirical illustration of the panel data analysis, we draw confidence bands for the density of the total factor productivity in a manufacturing industry in Chile.