Tests for monotonicity of a regression mean with guaranteed level
Tests for monotonicity of a regression mean with guaranteed level
复制标题
具有保证水平的回归均值的单调性测试
DOI：
10.1093/biomet/87.3.663
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发表时间：
2000
期刊：
影响因子：
2.7
通讯作者：
Inge Koch
中科院分区：
文献类型：
--
作者：
I. Gijbels;P. Hall;M. C. Jones;Inge Koch
本文提出了一种检验具有保证水平回归均值单调性的非参数方法。该程序基于响应变量的观测值差异的符号。当回归函数为常数时，该测试针对最困难的零假设进行校准，并在此上下文中产生精确的测试。一般来说，这个测试是保守的。该检验的有效性良好，可与其他非参数检验相比较。证明了测试过程对某些局部备选方案的渐近幂为1。该方法对重尾误差分布具有较强的鲁棒性，即使误差是柯西分布，也能保持较好的功率。提供了一个模拟研究来证明测试过程的有限样本行为。
In this paper a nonparametric procedure for testing for monotonicity of a regression mean with guaranteed level is proposed. The procedure is based on signs of differences of observations from the response variable. The test is calibrated against the most difficult null hypothesis, when the regression function is constant, and produces an exact test in this context. In general, the test is conservative. The power of the test is good, and comparable with that of other nonparametric tests. It is shown that the testing procedure has asymptotic power 1 against certain local alternatives. The method is also robust against heavy-tailed error distributions, and even maintains good power when the errors are for example Cauchy distributed. A simulation study is provided to demonstrate finite-sample behaviour of the testing procedure.