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Testing Monotonicity of Regression
A. W. Bowman, M. C. Jones and I. Gijbels
Journal of Computational and Graphical Statistics
Vol. 7, No. 4 (Dec., 1998), pp. 489-500
Published by: Taylor & Francis, Ltd. on behalf of the American Statistical Association, Institute of Mathematical Statistics, and Interface Foundation of America
Stable URL: http://www.jstor.org/stable/1390678
Page Count: 12
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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.
Journal of Computational and Graphical Statistics © 1998 American Statistical Association