
@misc{costa_novel_2025,
	title = {A novel framework for quantifying nominal outlyingness},
	url = {http://arxiv.org/abs/2408.07463},
	doi = {10.48550/arXiv.2408.07463},
	abstract = {Outlier detection is an important data mining tool that becomes particularly challenging when dealing with nominal data. First and foremost, flagging observations as outlying requires a well-defined notion of nominal outlyingness. This paper presents a definition of nominal outlyingness and introduces a general framework for quantifying outlyingness of nominal data. The proposed framework makes use of ideas from the association rule mining literature and can be used for calculating scores that indicate how outlying a nominal observation is. Methods for determining the involved hyperparameter values are presented and the concepts of variable contributions and outlyingness depth are introduced, in an attempt to enhance interpretability of the results. The proposed framework is evaluated on both synthetic and real-world data sets, demonstrating comparable performance to state-of-the-art frequent pattern mining algorithms and even outperforming them in certain cases. The ideas presented can serve as a tool for assessing the degree to which an observation differs from the rest of the data, under the assumption of sequences of nominal levels having been generated from a Multinomial distribution with varying event probabilities.},
	urldate = {2025-03-18},
	publisher = {arXiv},
	author = {Costa, Efthymios and Papatsouma, Ioanna},
	month = feb,
	year = {2025},
	note = {arXiv:2408.07463},
	keywords = {Statistics - Methodology},
	file = {Full Text PDF:C\:\\Users\\ec1917\\Zotero\\storage\\CZ66RHJW\\Costa and Papatsouma - 2025 - A novel framework for quantifying nominal outlyingness.pdf:application/pdf;Snapshot:C\:\\Users\\ec1917\\Zotero\\storage\\8J9RSDJW\\2408.html:text/html},
}

@article{sison_simultaneous_1995,
	title = {Simultaneous {Confidence} {Intervals} and {Sample} {Size} {Determination} for {Multinomial} {Proportions}},
	volume = {90},
	issn = {0162-1459},
	doi = {10.2307/2291162},
	abstract = {Simultaneous confidence interval procedures for multinomial proportions are used in many areas of science. In this article two new simultaneous confidence interval procedures are introduced. Numerical results are presented to evaluate these procedures and compare their performance with established methods that have been used in statistical literature. From the results presented in this article, it is evident that the new procedures are more accurate than the established ones, where the accuracy of the procedure is measured by the volume of the confidence region corresponding to the nominal coverage probability and the probability of coverage it achieves. In the sample size determination problem, the new procedures provide a sizable amount of savings as compared to the procedures that have been used in many applications. Because both procedures performed equally well, the procedure that requires the least amount of computing time is recommended.},
	number = {429},
	journal = {Journal of the American Statistical Association},
	author = {Sison, Cristina P. and Glaz, Joseph},
	year = {1995},
	pages = {366--369},
	file = {Full Text PDF:C\:\\Users\\ec1917\\Zotero\\storage\\Y3JRWAUA\\Sison and Glaz - 1995 - Simultaneous Confidence Intervals and Sample Size Determination for Multinomial Proportions.pdf:application/pdf},
}

@article{hanley_meaning_1982,
	title = {The meaning and use of the area under a receiver operating characteristic ({ROC}) curve},
	volume = {143},
	issn = {0033-8419},
	doi = {10.1148/radiology.143.1.7063747},
	abstract = {A representation and interpretation of the area under a receiver operating characteristic (ROC) curve obtained by the "rating" method, or by mathematical predictions based on patient characteristics, is presented. It is shown that in such a setting the area represents the probability that a randomly chosen diseased subject is (correctly) rated or ranked with greater suspicion than a randomly chosen non-diseased subject. Moreover, this probability of a correct ranking is the same quantity that is estimated by the already well-studied nonparametric Wilcoxon statistic. These two relationships are exploited to (a) provide rapid closed-form expressions for the approximate magnitude of the sampling variability, i.e., standard error that one uses to accompany the area under a smoothed ROC curve, (b) guide in determining the size of the sample required to provide a sufficiently reliable estimate of this area, and (c) determine how large sample sizes should be to ensure that one can statistically detect differences in the accuracy of diagnostic techniques.},
	language = {eng},
	number = {1},
	journal = {Radiology},
	author = {Hanley, J. A. and McNeil, B. J.},
	year = {1982},
	pages = {29--36},
}
