Testing Monotonicity of Regression
提出一种基于临界带宽的回归函数单调性检验方法，通过自助法获取检验统计量的零分布，适用于方差为均值函数或同方差情形，模拟和实例验证了方法的有效性。
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.