Bowman, A. W.; Jones, M. C. and Gijbels, I.
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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.
|Item Type:||Journal Article|
|Copyright Holders:||1998 American Statistical Association , Institute of Mathematical Statistics|
|Keywords:||bootstrap; critical bandwidth; local linear fitting; multimodality testing; smoothing|
|Academic Unit/Department:||Mathematics, Computing and Technology > Mathematics and Statistics|
|Depositing User:||Sarah Frain|
|Date Deposited:||04 May 2011 13:21|
|Last Modified:||04 May 2011 13:21|
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