Composite versus model-averaged quantile regression.

Abstract The composite quantile estimator is a robust and efficient alternative to the least-squares estimator in linear models. However, it is computationally demanding when the number of quantiles is large. We consider a model-averaged quantile estimator as a computationally cheaper alternative. We derive its asymptotic properties in high-dimensional linear models and compare its performance to the composite quantile estimator in both low- and high-dimensional settings. We also assess the effect on efficiency of using equal weights, theoretically optimal weights, and estimated optimal weights for combining the different quantiles. None of the estimators dominates in all settings under consideration, thus leaving room for both model-averaged and composite estimators, both with equal and estimated optimal weights in practice. Highlights • Comparing model averaged and composite quantile regression estimators. • Investigating properties of model averaged quantile estimators in high dimensions. • Studying the effect of the weight choice (estimated, optimal, equal weights). [ABSTRACT FROM AUTHOR]