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Abstract This article provides a test of monotonicity of a regression function. The test is based on the size of a “critical” bandwidth, the amount of smoothing necessary to force a nonparametric regression estimate to be monotone. It is analogous to Silverman's test of multimodality in density estimation. Bootstrapping is used to provide a null distribution for the test statistic. The methodology is particularly simple in regression models in which the variance is a specified function of the mean, but we also discuss in detail the homoscedastic case with unknown variance. Simulation evidence indicates the usefulness of the method. Two examples are given.
Bowman et al. (Tue,) studied this question.