Abstract: Model selection for quantile regression is a challenging problem. In addition to the well-known general difficulty of model selection uncertainty, when quantiles at multiple probability levels are of interest, typically a single candidate does not serve all of them simultaneously. In this paper, we propose methods to combine quantile estimators. Oracle inequalities show that, at each given probability level, the combined estimators automatically perform nearly as well as the best candidate. Simulation and examples show that the proposed model combination approach often leads to a substantial gain in accuracy under global measures of performance.
Key words and phrases: Adaptive quantile regression, aggregation of estimators, model combination.