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

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.