Robust Goodness-of-Fit Tests for Machine Learning Quantiles

• Faculty of Economics and Business, University of Amsterdam, Amsterdam, Netherlands [s.c.barendse@uva.nl]

Keywords: machine learning – quantile – quantile regression – goodness-of-fit tests

1 Abstract

We propose a novel set of goodness-of-fit tests for quantile models. The tests are locally robust to the estimation error which appears due to the pre-estimation of the parameters of the quantile model and utilize sample-splitting techniques. Consequently, our tests remain valid when the model is estimated using modern machine learning methods, which are typically high-dimensional and converge at slow rates. Importantly, our tests do not require any additional estimation steps other than the quantile models of interest, which facilitates implementation. We study the size and power properties of our tests in a simulation study.