Testing monotonicity via local least concave majorants
Testing monotonicity via local least concave majorants
复制标题
通过局部最小凹主函数测试单调性
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
C. Durot
中科院分区：
文献类型：
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作者：
N. Akakpo;F. Balabdaoui;C. Durot
我们提出了一种新的测试程序，用于检测嵌入在白色噪声中的信号的局部偏离单调性。事实上，我们同时执行几个测试，旨在检测偏离的集成信号在不同的大小和本地化的各种间隔。这些局部测试中的每一个都依赖于估计积分信号到某个区间的限制与其最小凹优量之间的距离。我们的测试可以很容易地实现，并证明了实现最佳的均匀分离率，同时为广泛的H”{o}lderian的替代品。此外，我们展示了如何将此测试扩展到具有未知方差的高斯回归框架。仿真研究证实了我们的程序在实践中的良好性能。
We propose a new testing procedure for detecting localized departures from monotonicity of a signal embedded in white noise. In fact, we perform simultaneously several tests that aim at detecting departures from concavity for the integrated signal over various intervals of different sizes and localizations. Each of these local tests relies on estimating the distance between the restriction of the integrated signal to some interval and its least concave majorant. Our test can be easily implemented and is proved to achieve the optimal uniform separation rate simultaneously for a wide range of H"{o}lderian alternatives. Moreover, we show how this test can be extended to a Gaussian regression framework with unknown variance. A simulation study confirms the good performance of our procedure in practice.