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    Estimating a common period for a set of irregularly sampled functions with applications to periodic variable star data

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    Author
    Long, James P.; Chi, Eric C.; Baraniuk, Richard G.
    Date
    2016
    Abstract
    We consider the problem of estimating a common period for a set of functions sampled at irregular intervals. The motivating problem arises in astronomy, where the functions represent a star’s observed brightness over time through different photometric filters. While current methods perform well when the brightness is sampled densely enough in at least one filter, they break down when no brightness function is densely sampled. In this paper we introduce two new methods for period estimation in this important latter case. The first, multiband generalized Lomb–Scargle (MGLS), extends the frequently used Lomb–Scargle method to naïvely combine information across filters. The second, penalized generalized Lomb–Scargle (PGLS), builds on MGLS by more intelligently borrowing strength across filters. Specifically, we incorporate constraints on the phases and amplitudes across the different functions using a nonconvex penalized likelihood function. We develop a fast algorithm to optimize the penalized likelihood that combines block coordinate descent with the majorization–minimization (MM) principle. We test and validate our methods on synthetic and real astronomy data. Both PGLS and MGLS improve period estimation accuracy over current methods based on using a single function; moreover, PGLS outperforms MGLS and other leading methods when the functions are sparsely sampled.
    Citation
    Long, James P., Chi, Eric C. and Baraniuk, Richard G.. "Estimating a common period for a set of irregularly sampled functions with applications to periodic variable star data." The Annals of Applied Statistics, 10, no. 1 (2016) Project Euclid: 165-197. https://doi.org/10.1214/15-AOAS885.
    Published Version
    https://doi.org/10.1214/15-AOAS885
    Keyword
    astrostatistics; penalized likelihood; period estimation; functional data; MM algorithm; More... block coordinate descent Less...
    Type
    Journal article
    Publisher
    Project Euclid
    Citable link to this page
    https://hdl.handle.net/1911/94215
    Rights
    Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
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    • ECE Publications [1443]
    • Faculty Publications [4988]

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    Home | FAQ | Contact Us | Privacy Notice | Accessibility Statement
    Managed by the Digital Scholarship Services at Fondren Library, Rice University
    Physical Address: 6100 Main Street, Houston, Texas 77005
    Mailing Address: MS-44, P.O.BOX 1892, Houston, Texas 77251-1892
    Site Map