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

## TL;DR

This paper explores how standardizing periodograms with training noise data can improve sinusoid detection in colored noise, with applications to exoplanet detection, balancing false alarms and detection power.

## Contribution

It introduces a method for standardizing periodograms using training data to enhance detection performance in colored noise, including analytical and numerical validation.

## Key findings

- Standardization can produce powerful constant false alarm rate tests.
- Theoretical results match numerical simulations for moderate sample sizes.
- Application demonstrated in exoplanet detection from radial velocity data.

## 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.