Why is linear quantile regression empirically successful: A possible explanation

Abstract

Many quantities describing the physical world are related to each other. As a result, often, when we know the values of certain quantities x1,…, xn, we can reasonably well predict the value of some other quantity y. In many application, in addition to the resulting estimate for y, it is also desirable to predict how accurate is this approximate estimate, i.e., what is the probability distribution of different possible values y. It turns out that in many cases, the quantiles of this distribution linearly depend on the values x1,…, xn. In this paper, we provide a possible theoretical explanation for this somewhat surprising empirical success of such linear quantile regression.