Sensitivity analysis for quantile regression

摘要

In this paper, we explore sensitivity analysis for quantile regression and confront it with diagnostic testing. Every model is misspecified (in the sense that no model coincides with the data-generating process), but a model is useful if the parameters of interest (the focus) are not sensitive to small perturbations of the underlying assumptions. Magnus and Vasnev (2007) found that in the case of mean regression (and more generally in a maximum likelihood framework) both, sensitivity and diagnostic, are important and often (asymptotically) independent. One expects similar result for quantile regression as well. However, the relationship between sensitivity and diagnostic varies for different quantiles. We introduce a sensitivity statistic for quantile regression, compare it with the mean regression sensitivity and look at its performance in simulations.