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Statistical inference for evolving periodic functions

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  • Marc G. Genton
  • Peter Hall

Abstract

Summary. In the study of variable stars, where the light reaching an observer fluctuates over time, it can be difficult to explain the nature of the variation unless it follows a regular pattern. In this respect, so‐called periodic variable stars are particularly amenable to analysis. There, radiation varies in a perfectly periodic fashion, and period length is a major focus of interest. We develop methods for conducting inference about features that might account for departures from strict periodicity. These include variation, over time, of the period or amplitude of radiation. We suggest methods for estimating the parameters of this evolution, and for testing the hypothesis that the evolution is present. This problem has some unusual features, including subtle issues of identifiability.

Suggested Citation

  • Marc G. Genton & Peter Hall, 2007. "Statistical inference for evolving periodic functions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(4), pages 643-657, September.
  • Handle: RePEc:bla:jorssb:v:69:y:2007:i:4:p:643-657
    DOI: 10.1111/j.1467-9868.2007.00604.x
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    Cited by:

    1. Oliver Linton & Michael Vogt, 2012. "Nonparametric estimation of a periodic sequence in the presence of a smooth trend," CeMMAP working papers 23/12, Institute for Fiscal Studies.
    2. Michael Vogt & Oliver Linton, 2014. "Nonparametric estimation of a periodic sequence in the presence of a smooth trend," Biometrika, Biometrika Trust, vol. 101(1), pages 121-140.
    3. Zheng Xu, 2016. "An alternative circular smoothing method to nonparametric estimation of periodic functions," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(9), pages 1649-1672, July.
    4. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.

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