A simple test for comparing regression curves versus one-sided alternatives

Robust testing for superiority between two regression curves

“…As mentioned in the introduction, we wish to develop a class of robust tests for H 0 versus H 1 in (2) which allows to detect root−n local alternatives. As in Neumeyer and Pardo-Fernández (2009), let m be any function such that m 1 (x) ≤ m(x) ≤ m 2 (x), for all x ∈ R, and define the random variables, for j = 1, 2,…”

“…In this section, we present the results of a simulation study devoted to illustrate the finite-sample performance of the testing procedure described in Section 3 and to compare its behaviour with that of the test defined in Neumeyer and Pardo-Fernández (2009) and the covariate-matched Wilcoxon-Mann-Whitney statistic given in Koul and Schick (1997). More specifically, for the robust procedure, we use the approximation of the critical values given in Remark 2.…”

“…When second moments exist, the problem of testing equality of two regression curves versus one-sided alternatives has been considered by several authors such as Hall et al (1997), Schick (1997, 2003) and Neumeyer and Dette (2005), who extended the test proposed in Speckman et al (2003) to allow for heteroscedasticity. On the other hand, Neumeyer and Pardo-Fernández (2009) introduced a simple root−n test statistic based on the comparison of the sample averages of the estimated residuals, which were computed with respect to a linear convex combination of the kernel regression estimators obtained from each sample.…”

“…The aim of this paper is to propose a class of robust tests for H 0 versus H 1 in (2) which allows for possibly different covariate densities and error densities in the two populations. Our proposal combines the ideas of robust smoothing with those given in Neumeyer and Pardo-Fernández (2009) to obtain a procedure detecting root−n alternatives. In Section 2, we recall the definition of the robust estimators.…”

A Non‐parametric ANOVA‐type Test for Regression Curves Based on Characteristic Functions

“…The majority of the available papers either are devoted to the comparison of only two curves or impose some restrictive assumptions such as fixed design, equal sample sizes, identical design points and homoscedasticity of the residuals. Examples of such works include Delgado (1993), Kulasekera (1995), Munk & Dette (1998), Neumeyer & Pardo-Fernández (2009) and Srihera & Stute (2010), among many others. To the best of our knowledge, the most related works to ours are the papers of Neumeyer & Dette (2003) and of Pardo-Fernández et al (2007).…”