Why Is Linear Quantile Regression Empirically Successful: A Possible Explanation

Authors

Hung T. Nguyen, New Mexico State University - Main CampusFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Songsak Sriboonchitta, Chiang Mai UniversityFollow

Publication Date

5-2015

Comments

Technical Report: UTEP-CS-15-42

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, ..., x_n, 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, ..., x_n. In this paper, we provide a possible theoretical explanation for this somewhat surprising empirical success of such linear quantile regression.