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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
DOI: 10.2307/1390678
Stable URL: http://www.jstor.org/stable/1390678
Page Count: 12
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Testing Monotonicity of Regression
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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.

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