The independence process in conditional quantile location-scale models and an application to testing for monotonicity
Abstract
In this paper the nonparametric quantile regression model is considered in a location-scale context. The asymptotic properties of the empirical independence process based on covariates and estimated residuals are investigated. In particular an asymptotic expansion and weak convergence to a Gaussian process are proved. The results can, on the one hand, be applied to test for validity of the location-scale model. On the other hand, they allow to derive various specification tests in conditional quantile location-scale models. In detail a test for monotonicity of the conditional quantile curve is investigated. For the test for validity of the location-scale model as well as for the monotonicity test smooth residual bootstrap versions of Kolmogorov-Smirnov and Cramer-von Mises type test statistics are suggested. We give rigorous proofs for bootstrap versions of the weak convergence results. The performance of the tests is demonstrated in a simulation study.
Cite
@article{arxiv.1609.07696,
title = {The independence process in conditional quantile location-scale models and an application to testing for monotonicity},
author = {Melanie Birke and Natalie Neumeyer and Stanislav Volgushev},
journal= {arXiv preprint arXiv:1609.07696},
year = {2016}
}