Bootstrap tests for nonparametric comparison of regression curves with dependent errors

Abstract

In this paper, the problem of testing the equality of regression curves with dependent data is studied. Several methods based on nonparametric estimators of the regression function are described. In this setting, the distribution of the test statistic is frequently unknown or difficult to compute, so an approximate test based on the asymptotic distribution of the statistic can be considered. Nevertheless, the asymptotic properties of the methods proposed in this work have been obtained under independence of the observations, and just one of these methods was studied in a context of dependence as reported by Vilar-Fernández and González-Manteiga (Statistics 58(2):81–99, 2003). In addition, the distribution of these test statistics converges to the limit distribution with convergence rates usually rather slow, so that the approximations obtained for reasonable sample sizes are not satisfactory. For these reasons, many authors have suggested the use of bootstrap algorithms as an alternative approach. Our main concern is to compare the behavior of three bootstrap procedures that take into account the dependence assumption of the observations when they are used to approximate the distribution of the test statistics considered. A broad simulation study is carried out to observe the finite sample performance of the analyzed bootstrap tests.