Bowman, A. W.; Jones, M. C. and Gijbels, I.
Testing monotonicity of regression.
Journal of Computational and Graphical Statistics, 7(4) pp. 489–500.
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.
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