Complete Subset Averaging for Quantile Regressions

We propose a novel conditional quantile prediction method based on complete subset averaging (CSA) for quantile regressions. All models under consideration are potentially misspecified, and the dimension of regressors goes to infinity as the sample size increases. Since we average over the complete subsets, the number of models is much larger than the usual model averaging method which adopts sophisticated weighting schemes. We propose to use an equal weight but select the proper size of the complete subset based on the leave-one-out cross-validation method. Building upon the theory of Lu and Su (2015, Journal of Econometrics 188, 40-58), we investigate the large sample properties of CSA and show the asymptotic optimality in the sense of Li (1987, Annals of Statistics 15, 958-975) We check the finite sample performance via Monte Carlo simulations and empirical applications.