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Bias-corrected maximum likelihood estimation of the parameters of the complex Bingham distribution. (English) Zbl 1381.62049

Summary: In this paper, some bias correction methods are considered for parameter estimation of the complex Bingham distribution. The first method relies on the bias correction formula proposed by G. M. Cordeiro and R. Klein [Stat. Probab. Lett. 19, No. 3, 169–176 (1994; Zbl 0791.62087)]. The second method uses the formulas proposed by A. Kume and the last author [ibid. 77, No. 8, 832–837 (2007; Zbl 1373.62239)] for calculating the derivatives of the log likelihood function. The third method is based on the saddlepoint approximation proposed by A. Kume and the last author [Biometrika 92, No. 2, 465–476 (2005; Zbl 1094.62063)]. Bootstrap bias correction methods due to B. Efron are also considered [Ann. Stat. 7, 1–26 (1979; Zbl 0406.62024)]. Simulation experiments are used to compare the bias correction methods. In all cases, the analytical and bootstrap bias correction methods have smaller mean square errors. Since the dominant eigenvalue is used to obtain the mean shape, which has practical relevance, it is a key issue for comparing the estimators. The numerical results indicate that the bootstrap methods have a slightly better performance for the dominant eigenvalue.

MSC:

62F10 Point estimation
60E05 Probability distributions: general theory
62H11 Directional data; spatial statistics
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References:

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