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

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.