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

Hamid Haji Aghabozorgi () and Farzad Eskandari ()
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Hamid Haji Aghabozorgi: Allameh Tabataba’i University
Farzad Eskandari: Allameh Tabataba’i University

Statistical Papers, 2024, vol. 65, issue 2, No 8, 705-736

Abstract: 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.

Keywords: Bivariate ranked set sampling; EM algorithm; Mixture models; Model-based clustering; 62D05; 62H30 (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00362-023-01411-6

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