Testing Equality of Nonparametric Quantile Regression Functions

Abstract

This article proposes a new approach for testing the equality of nonparametric quantile regression functions based on marked empirical processes. We develop test statistics that posses better Type I and power properties in comparison to all available procedures in the literature. Simulation results also indicate that our tests have superior local power properties over existing tests. A data analysis is given which highlights the usefulness of the proposed methodology.

Robust testing to compare regression curves

“…Under a partly linear regression model, Bianco et al (2006) proposed a test to study if the nonparametric component equals a fixed given function, while Boente et al (2013) considered the hypothesis that the nonparametric function is a linear function under a generalized partially linear model. On the other hand, Sun (2006), Dette et al (2011Dette et al ( , 2013 and Kuruwita et al (2014) considered the problem of comparing quantile functions. Sun (2006) proposed a test based on an orthogonal moment condition of residuals which converges at non-parametric rate, while Dette et al (2011Dette et al ( , 2013 provided a test based on the L 2 −distance between non-crossing non-parametric estimates of the quantile curves, the latter one detects alternatives at rate root-n.…”

“…Sun (2006) proposed a test based on an orthogonal moment condition of residuals which converges at non-parametric rate, while Dette et al (2011Dette et al ( , 2013 provided a test based on the L 2 −distance between non-crossing non-parametric estimates of the quantile curves, the latter one detects alternatives at rate root-n. Finally, the proposal in Kuruwita et al (2014) is based on a marked empirical process of the residuals detecting also root-n alternatives. When considering the problem of comparing two regression functions versus a one-sided alternative, Boente and Pardo-Fernández (2016) proposed a test statistic that uses a bounded score function and the residuals obtained from a robust estimate for the regression function under the null hypothesis.…”

Robust nonparametric regression for testing the equality of nonparametric regression curves

“…Such issues have been addressed by few researchers. [8] employed a marked empirical process to test the equality of nonparametric regression curves and compared the efficiency of the test statistics in case of heavy-tailed errors. [9] tested the equality of two parametric quantile regression curves and compared the conditional quantile regression and the conditional mean regression in case errors were heavy-tailed and outliers were present in the data.…”