Percentile-t Bootstrap Confidence Intervals for Period Using Periodogram

Abstract

The magnitude of light intensity of many stars varies over time in a periodic way. Therefore, estimation of period and making inference about this parameter are of great interest in astronomy. The periodogram can be used to estimate period, properly. Bootstrap confidence intervals for period suggested here, are based on using the periodogram and constructed by percentile-t methods. We prove that the equal-tailed percentile-t bootstrap confidence intervals for period have an error of order n ⁻¹. We also show that the symmetric percentile-t bootstrap confidence intervals reduce the error to order n ⁻², and hence have a better performance. Finally, we assess the theoretical results by conducting a simulation study, compare the results with the coverages of percentile bootstrap confidence intervals for period and then analyze a real data set related to the eclipsing system R Canis Majoris collected by Shiraz Biruni Observatory.

Keywords:

• Astronomy
• Bootstrap confidence interval
• Light-curve
• Percentile-t methods
• Period
• Periodogram

Mathematics Subject Classification:

• 62G09
• 85A35

Acknowledgments

We are grateful to Dr. Torabi for his helpful comments about the article, especially about the real data analysis. This work was partially supported by Shahid Beheshti University.