Title: A study of periodograms standardized using training data sets and application to exoplanet detection,
Abstract: 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.