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Estimation of finite mixture models of skew-symmetric circular distributions

Author

Listed:
  • Yoichi Miyata

    (Takasaki City University of Economics)

  • Takayuki Shiohama

    (Tokyo University of Science)

  • Toshihiro Abe

    (Nanzan University)

Abstract

Analysis of circular data is challenging, since the usual statistical methods are unsuitable and it is necessary to use circular periodic probabilistic models. Because some actual circular datasets exhibit asymmetry and/or multimodality, finite mixtures of symmetric circular distributions to model and fit these data have been investigated. However, it is necessary to question the predominant assumption that each component in the finite mixture model is symmetric. In this study, we consider a finite mixture model of possibly skewed circular distributions and discuss the expectation-maximization (EM) algorithm for the maximum likelihood estimate. It is shown that the maximum likelihood estimator is strongly consistent under some suitable conditions in a finite mixture of skew-symmetric circular distributions. A modified M-step in the EM algorithm is proposed in order to estimate the unknown parameter vectors effectively. To investigate the performance of our proposed model with its estimation procedure, we provide a numerical example as well as data analysis using the records of the time of day of fatal traffic accidents.

Suggested Citation

  • Yoichi Miyata & Takayuki Shiohama & Toshihiro Abe, 2020. "Estimation of finite mixture models of skew-symmetric circular distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(8), pages 895-922, November.
    • Handle: RePEc:spr:metrik:v:83:y:2020:i:8:d:10.1007_s00184-019-00756-z
    DOI: 10.1007/s00184-019-00756-z
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    References listed on IDEAS

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    1. Karlis, Dimitris & Xekalaki, Evdokia, 2003. "Choosing initial values for the EM algorithm for finite mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 41(3-4), pages 577-590, January.
    2. Toshihiro Abe & Arthur Pewsey, 2011. "Sine-skewed circular distributions," Statistical Papers, Springer, vol. 52(3), pages 683-707, August.
    3. Kentaro Tanaka, 2009. "Strong Consistency of the Maximum Likelihood Estimator for Finite Mixtures of Location–Scale Distributions When Penalty is Imposed on the Ratios of the Scale Parameters," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 171-184, March.
    4. R. C. H. Cheng & W. B. Liu, 2001. "The Consistency of Estimators in Finite Mixture Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(4), pages 603-616, December.
    5. Melnykov, Volodymyr & Melnykov, Igor, 2012. "Initializing the EM algorithm in Gaussian mixture models with an unknown number of components," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1381-1395.
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    Cited by:

    1. Abe, Toshihiro & Miyata, Yoichi & Shiohama, Takayuki, 2023. "Bayesian estimation for mode and anti-mode preserving circular distributions," Econometrics and Statistics, Elsevier, vol. 27(C), pages 136-160.
    2. Yoichi Miyata & Takayuki Shiohama & Toshihiro Abe, 2023. "Identifiability of Asymmetric Circular and Cylindrical Distributions," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(2), pages 1431-1451, August.
    3. Arthur Pewsey & Eduardo García-Portugués, 2021. "Recent advances in directional statistics," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 1-58, March.

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