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Statistical inference for evolving periodic functions

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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.

Keywords: Amplitude; Astronomy; Bandwidth; Bootstrap; Kernel methods; Light curve; Non-parametric regression; Parametric inference; Time transformation

Document Type: Research Article


Affiliations: 1: University of Geneva, Switzerland, Texas A&M University, College Station, USA, and Australian National University, Canberra, Australia 2: Australian National University, Canberra, Australia

Publication date: September 1, 2007


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