Robust fitting for pulsar timing analysis

Yidi Wang, Michael Keith, Benjamin Stappers, Wei Zheng

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    We introduce a robust fitting method into pulsar timing analysis to cope with the non-Gaussian noise. The general maximum likelihood estimator (M-estimator) can resist the impact of non-Gaussian noise by employing convex and bounded loss functions. Three loss functions, including the Huber function, the Bisquare function and the Welsch function, are investigated. The Shapiro–Wilk test is employed to test whether the uncertainty in the observed times of arrival is drawn from a non-Gaussian distribution. Two simulations, where the non-Gaussian distribution is modelled as contaminated Gaussian distributions, are performed. It is found that M-estimators are unbiased and could achieve a root-mean-square error smaller than that obtained by the least square (LS) at the cost of a slightly higher computation complexity in a non-Gaussian environment. M-estimators are also applied to the real timing data of PSR J1713+0747. The results have shown that the fitting results of M-estimators are more accurate than those of LS and are closer to the result of very long baseline interferometry.
    Original languageEnglish
    Pages (from-to)2637-2644
    Number of pages8
    JournalMonthly Notices of the Royal Astronomical Society
    Issue number3
    Early online date8 Mar 2017
    Publication statusPublished - Jul 2017


    • Methods
    • Data analysis
    • Pulsars


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