用训练数据集标准化周期图的研究和对系外行星探测的应用
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带有未知统计量时，正弦检测的困难在于控制测试结果的真实显着性水平。本文探讨了使用训练数据集的噪声，以改善这种控制的可能性。具体来说，我们分析了各种检测器的性能{适用于}使用训练数据集标准化的周期图。重点放在稀疏检测在傅立叶域和在实践中提供的训练集的必要有限的大小所构成的限制。我们研究了由此产生的误报率和检测率，并表明在某些情况下，标准化导致强大的恒定误报率测试。这项研究既是分析性的，也是数字性的。虽然分析结果是在一个渐进的制度，数值结果表明，理论准确地描述了中等大的样本量的测试行为。在整个文件中，所考虑的周期图标准化的应用程序提出的径向速度数据的系外行星检测。
英文摘要：
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.
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