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Clustering and estimation of finite mixture models under bivariate ranked set sampling with application to a breast cancer study

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  • Hamid Haji Aghabozorgi

    (Allameh Tabataba’i University)

  • Farzad Eskandari

    (Allameh Tabataba’i University)

Abstract

In the literature on modeling heterogeneous data via mixture models, it is generally assumed that the samples are drawn from the underlying population using the simple random sampling (SRS) technique. This study exploits the bivariate ranked set sampling (BVRSS) technique to learn finite mixture models. We generalize the expectation-maximization (EM) algorithm under univariate RSS to the bivariate case. Computationally, through a simulation study under a noisy setting, we compare the performance of the proposed rank-based estimators with that of the SRS-based competitors in estimating unknown parameters and cluster assignments. The proposed methodology is applied to a breast cancer data set to diagnose malignant or benign tumors in patients. The results showed that the extra rank information in BVRSS samples leads to a better inference about the unknown features of mixture models.

Suggested Citation

  • Hamid Haji Aghabozorgi & Farzad Eskandari, 2024. "Clustering and estimation of finite mixture models under bivariate ranked set sampling with application to a breast cancer study," Statistical Papers, Springer, vol. 65(2), pages 705-736, April.
    • Handle: RePEc:spr:stpapr:v:65:y:2024:i:2:d:10.1007_s00362-023-01411-6
    DOI: 10.1007/s00362-023-01411-6
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    References listed on IDEAS

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    1. Armin Hatefi & Mohammad Jafari Jozani & Omer Ozturk, 2015. "Mixture Model Analysis of Partially Rank-Ordered Set Samples: Age Groups of Fish from Length-Frequency Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 848-871, September.
    2. Hatefi, Armin & Jafari Jozani, Mohammad, 2013. "Fisher information in different types of perfect and imperfect ranked set samples from finite mixture models," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 16-31.
    3. Olvi L. Mangasarian & W. Nick Street & William H. Wolberg, 1995. "Breast Cancer Diagnosis and Prognosis Via Linear Programming," Operations Research, INFORMS, vol. 43(4), pages 570-577, August.
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