标题： 使用训练数据集标准化的周期图研究及其在系外行星检测中的应用 显示英文标题

标题： A study of periodograms standardized using training data sets and application to exoplanet detection

摘要： 当影响时间序列的噪声是彩色的且统计特性未知时，正弦波检测的一个困难在于控制测试结果的真实显著性水平。 本文研究了使用噪声的训练数据集来改善此控制的可能性。 具体而言，我们分析了各种检测器{应用于}使用训练数据集进行标准化的周期图性能。 重点放在傅里叶域中的稀疏检测以及由于实际中可用的训练集大小必然有限所带来的限制上。 我们研究了由此产生的虚警率和检测率，并表明在某些情况下标准化会导致强大的恒定虚警率测试。 该研究既有分析性也有数值性。 尽管分析结果是在渐近 regime 中推导出来的，但数值结果表明理论对于中等大的样本量准确描述了测试的行为。 在整篇论文中，展示了所考虑的周期图标准化在径向速度数据中用于系外行星检测的应用。 显示英文摘要

摘要： When the noise affecting time series is colored with unknown statistics, a difficulty for sinusoid detection is to control the true significance level of the test outcome. This paper investigates the possibility of using training data sets of the noise to improve this control. Specifically, we analyze the performances of various detectors {applied to} periodograms standardized using training data sets. Emphasis is put on sparse detection in the Fourier domain and on the limitation posed by the necessarily finite size of the training sets available in practice. We study the resulting false alarm and detection rates and show that standardization leads in some cases to powerful constant false alarm rate tests. The study is both analytical and numerical. Although analytical results are derived in an asymptotic regime, numerical results show that theory accurately describes the tests' behaviour for moderately large sample sizes. Throughout the paper, an application of the considered periodogram standardization is presented for exoplanet detection in radial velocity data.