Hotelling tubes, confidence bands and conformal inference

Abstract

AbstractStochastic frontier models and methods as pioneered by Peter Schmidt in Aigner et al. (J Econom 6:21–37, 1977), Horrace and Schmidt (J Product Anal 7:257–282, 1996), Amsler et al. (J Econom 190:280–288, 2016) constitute a rare departure from the usual econometric obsession with models for conditional means. They also provided an early stimulus for the development of quantile regression methods. After a brief tutorial on Hotelling tube methods for constructing confidence bands for nonparametric quantile regression, strengthened performance guarantees for such bands are described based on recent developments in conformal inference. These methods may be considered to be a rather idiosyncratic new approach to nonparametric inference for stochastic frontier models.