Extreme-value modelling for the significance assessment of periodogram peaks

TL;DR

This paper introduces a new method using generalized extreme-value distributions to accurately estimate the significance of peaks in periodograms, especially for high-confidence levels, with demonstrated stability and reliability.

Contribution

The paper presents a novel approach employing extreme-value theory for False Alarm Probability estimation in periodogram analysis, improving extrapolation and confidence interval derivation.

Findings

Method provides stable estimates against distributional deviations

Demonstrated effectiveness on simulated data

Validated on real star data from SDSS Stripe 82

Abstract

I propose a new procedure to estimate the False Alarm Probability, the measure of significance for peaks of periodograms. The key element of the new procedure is the use of generalized extreme-value distributions, the limiting distribution for maxima of variables from most continuous distributions. This technique allows reliable extrapolation to the very high probability levels required by multiple hypothesis testing, and enables the derivation of confidence intervals of the estimated levels. The estimates are stable against deviations from distributional assumptions, which are otherwise usually made either about the observations themselves or about the theoretical univariate distribution of the periodogram. The quality and the performance of the procedure is demonstrated on simulations and on two multimode variable stars from Sloan Digital Sky Survey Stripe 82.