On Properties of Percentile Bootstrap Confidence Intervals for Period Using Periodogram

Abstract

Periodic functions have many applications in astronomy. They can be used to model the magnitude of light intensity of the period variable stars that their brightness vary with time. Because the data related to the astronomical applications are commonly observed at the time points that are not regularly spaced, the use of the periodogram as a good tool for estimating period is highlighted. Our bootstrap inference about period is based on maximizing the periodogram and consists of percentile two-sided bootstrap confidence intervals construction for the true period. We also obtain their coverage levels theoretically, and discuss the benefit of double-bootstrap confidence intervals for the parameter by which the coverage levels are substantially improved. Precisely, we show that the coverage error of single-bootstrap confidence intervals is of order n ⁻¹, decreasing to order n ⁻² when applying double-bootstrap methods. The simulation study given here is a numerical assessment of the theoretical work.

Keywords:

• Astronomy
• Bootstrap confidence intervals
• Percentile method
• Period
• Periodic function
• Periodogram

Mathematics Subject Classification:

• 62G09
• 85A35

Acknowledgments

We are grateful to the three reviewers and Dr. Torabi for their helpful comments about the article.