We study the focused information criterion and frequentist model averaging and their application to post-model-selection inference for weighted composite quantile regression (WCQR) in the context of the additive partial linear models. With the non-parametric functions approximated by polynomial splines, we show that, under certain conditions, the asymptotic distribution of the frequentist model averaging WCQR-estimator of a focused parameter is a non-linear mixture of normal distributions. This asymptotic distribution is used to construct confidence intervals that achieve the nominal coverage probability. With properly chosen weights, the focused information criterion based WCQR estimators are not only robust to outliers and non-normal residuals but also can achieve efficiency close to the maximum likelihood estimator, without assuming the true error distribution. Simulation studies and a real data analysis are used to illustrate the effectiveness of the proposed procedure. © 2013 Board of the Foundation of the Scandinavian Journal of Statistics..
Bibliographical noteKAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): KUS-CI-016-04
Acknowledgements: This research was partially supported by Award Number KUS-CI-016-04, made by King Abdullah University of Science and Technology (KAUST). Huang's research was also partially supported by NSF (DMS-0907170, DMS-1007618, DMS-1208952), NCI (CA57030). Part of this work was carried out while Wang was a visiting Professor at KAUST.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.