# A Bootstrap Method for Sinusoid Detection in Colored Noise and Uneven Sampling. Application to Exoplanet Detection

## TL;DR

This paper introduces a bootstrap-based method for reliable sinusoid detection in uneven, colored noise time series, with applications to exoplanet detection, addressing false alarm rate estimation when limited noise data is available.

## Contribution

It develops a bootstrap approach combined with periodogram standardization and extreme value modeling to accurately estimate false alarm rates in challenging noise conditions.

## Key findings

- Effective FA rate estimation in uneven, colored noise scenarios.
- Improved detection reliability using generalized extreme value distributions.
- Successful application to exoplanet radial velocity data.

## Abstract

This study is motivated by the problem of evaluating reliable false alarm (FA) rates for sinusoid detection tests applied to unevenly sampled time series involving colored noise, when a (small) training data set of this noise is available. While analytical expressions for the FA rate are out of reach in this situation, we show that it is possible to combine specific periodogram standardization and bootstrap techniques to consistently estimate the FA rate. We also show that the procedure can be improved by using generalized extremevalue distributions. The paper presents several numerical results including a case study in exoplanet detection from radial velocity data.