INFERENCE FOR VON MISES MIXTURE IN MEAN DIRECTION AND CONCENTRATION PARAMETERS
Chen Jiahua(1),Li Pengfei(1),Tan Xianming(2)
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(1)Department of Statistical and Acturial Sciences, University of Waterloo, ON, Canada N2L 3G1; (2) LPMC and School of Mathematical Sciences, Nankai University, Tianjin 300071
The finite mixtures of von Mises distributions in both mean direction and concentration parameters are widely used in many disciplines, including astronomy, biology, ecology,geology and medicine. It is well known that the likelihood function is unbounded for any sample size. Hence, the ordinary maximum likelihood estimator (MLE) is not consistent. Similar to normal mixtures in both mean and variance parameters, this drawback of MLE will disappear by introducing a penalty function to the log-likelihood function or putting constraints on component concentration parameters (Chen et al., 2006 and Tan et al., 2006). In this paper, we prove that both of the penalized maximum likelihood estimator and the constrained maximum likelihood estimator are asymptotically consistent and efficient. The finite sample performance of penalized MLE and constrained MLE are compared with the moment estimator (Spur and Koutbeiy, 1991) through simulations. The PMLE is found to have the best performance in term of mean square error. A real data example is used to illustrate the proposed methods.
Chen Jiahua
, Li Pengfei
, Tan Xianming. , {{custom_author.name_en}}.
INFERENCE FOR VON MISES MIXTURE IN MEAN DIRECTION AND CONCENTRATION PARAMETERS. Journal of Systems Science and Mathematical Sciences, 2007, 27(1): 59-67 https://doi.org/10.12341/jssms08739
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