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This paper introduces a novel formulation of Fractionally Supervised Classification (FSC) tailored for maxima nominated samples, where observations are extreme order statistics rather than random samples. They address the limitations of existing FSC methods, which assume simple random sampling, by developing a latent representation that accounts for both the class membership of the observed maximum and the latent composition of the remaining units in the set. The resulting EM algorithm and weighted-likelihood FSC procedure for NS data demonstrate improved performance compared to misspecified alternatives, especially in rare-event scenarios.
Ignoring the rank information in maxima nominated samples can lead to substantial performance degradation in fractionally supervised classification, a problem this paper elegantly solves with a new EM algorithm.
Fractionally supervised classification (FSC) offers a flexible framework for combining labeled and unlabeled data in model-based classification, but existing formulations assume simple random sampling. In many applications, however, the retained observation is an extreme order statistic from a set rather than a randomly selected unit. This is particularly appealing when the target population is rare, since maxima nomination sampling (NS) can enrich the sample with the most informative observations, as in screening, environmental monitoring, repeated testing, and reliability studies. Under such designs, the likelihood function changes fundamentally, and the usual FSC EM construction is no longer valid. We develop FSC for nominated samples by introducing a latent representation that accounts for both the class membership of the observed maximum and the latent composition of the remaining units in the set. The resulting method yields a proper EM algorithm and a coherent weighted-likelihood FSC procedure for NS data. We present the methodology in general form, illustrate it for a rare-event contamination normal mixtures, and show through simulation that it substantially improves on the misspecified alternative by ignoring the extra rank information of such data. A real-data analysis demonstrates its practical value.
