Semiparametric model averaging for high-dimensional quantile regression with nonignorable nonresponse

Abstract: Model averaging has demonstrated superior performance for ensemble forecasting in high-dimensional framework, its extension to incomplete datasets remains a critical but underexplored challenge. Moreover, identifying the parsimonious model through averaging procedure in quantile regression demands urgent methodological innovation. In this paper, we propose a novel model averaging method for high-dimensional quantile regression with nonignorable missingness. The idea is to relax the parametric constraint on the conditional distribution of respondents, which is constructed through the two-phase scheme: (i) a semiparametric likelihood-based estimation for the missing mechanism, and (ii) a semiparametric weighting procedure to combine candidate models. One of pivotal advantages is our SMA estimator can asymptotically concentrate on the optimally correct model when the candidate set involves at least one correct model. Theoretical results show that the estimator achieves asymptotic optimality even under complex missingness conditions. Empirical conclusions illustrate the efficiency of the method.