Testing Monotonicity of Regression
- 1 December 1998
- journal article
- research article
- Published by Taylor & Francis in Journal of Computational and Graphical Statistics
- Vol. 7 (4) , 489-500
- https://doi.org/10.1080/10618600.1998.10474790
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.Keywords
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