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A Study of Periodograms Standardized Using Training Datasets and Application to Exoplanet Detection

机译：利用训练数据集标准化周期图的研究及其在系外行星探测中的应用

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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 datasets of the noise to improve this control. Specifically, we analyze the performances of various detectors applied to periodograms standardized using training datasets. 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’ behavior for moderately large sample sizes. Throughout the paper, an application of the considered periodogram standardization is presented for exoplanet detection in radial velocity data.
机译：当影响时间序列的噪声带有未知统计数据时，正弦波检测的困难在于控制测试结果的真实显着性水平。本文研究了使用噪声训练数据集来改善这种控制的可能性。具体而言，我们分析了使用训练数据集标准化的周期图所适用的各种检测器的性能。重点放在傅立叶域中的稀疏检测上，以及在实践中可用的训练集的必要有限大小所造成的限制。我们研究了由此产生的错误警报和检测率，并表明在某些情况下标准化导致了强大的恒定错误警报率测试。该研究是分析性的和数值性的。尽管分析结果是在渐近状态下得出的，但数值结果表明，该理论可以准确地描述中等大小样本的测试行为。整篇论文都介绍了考虑的周期图标准化在径向速度数据中系外行星探测中的应用。

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