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Period analysis of variable stars by robust smoothing

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  • Hee‐Seok Oh
  • Doug Nychka
  • Tim Brown
  • Paul Charbonneau

Abstract

Summary. The objective is to estimate the period and the light curve (or periodic function) of a variable star. Previously, several methods have been proposed to estimate the period of a variable star, but they are inaccurate especially when a data set contains outliers. We use a smoothing spline regression to estimate the light curve given a period and then find the period which minimizes the generalized cross‐validation (GCV). The GCV method works well, matching an intensive visual examination of a few hundred stars, but the GCV score is still sensitive to outliers. Handling outliers in an automatic way is important when this method is applied in a ‘data mining’ context to a vary large star survey. Therefore, we suggest a robust method which minimizes a robust cross‐validation criterion induced by a robust smoothing spline regression. Once the period has been determined, a nonparametric method is used to estimate the light curve. A real example and a simulation study suggest that the robust cross‐validation and GCV methods are superior to existing methods.

Suggested Citation

  • Hee‐Seok Oh & Doug Nychka & Tim Brown & Paul Charbonneau, 2004. "Period analysis of variable stars by robust smoothing," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(1), pages 15-30, January.
    • Handle: RePEc:bla:jorssc:v:53:y:2004:i:1:p:15-30
    DOI: 10.1111/j.1467-9876.2004.00423.x
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    Cited by:

    1. Hooper, Peter M., 2007. "Period analysis of variable stars: Temporal dependence and local optima," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6070-6083, August.
    2. Minji Lee & Zhihua Su, 2020. "A Review of Envelope Models," International Statistical Review, International Statistical Institute, vol. 88(3), pages 658-676, December.
    3. Lee, Jong Soo & Cox, Dennis D., 2010. "Robust smoothing: Smoothing parameter selection and applications to fluorescence spectroscopy," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3131-3143, December.
    4. Debruyne, Michiel & Christmann, Andreas & Hubert, Mia & Suykens, Johan A.K., 2010. "Robustness of reweighted Least Squares Kernel Based Regression," Journal of Multivariate Analysis, Elsevier, vol. 101(2), pages 447-463, February.
    5. Zhang, Likun & Castillo, Enrique del & Berglund, Andrew J. & Tingley, Martin P. & Govind, Nirmal, 2020. "Computing confidence intervals from massive data via penalized quantile smoothing splines," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    6. Michael Schomaker, 2012. "Shrinkage averaging estimation," Statistical Papers, Springer, vol. 53(4), pages 1015-1034, November.
    7. Yuan Xue & Xiangrong Yin, 2015. "Sufficient dimension folding for a functional of conditional distribution of matrix- or array-valued objects," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 27(2), pages 253-269, June.

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